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Open Access Article
1 - Analytical approach for the use of different gauges in bubble wakefield acceleration
Hitendra Malik Sonu Kumar Vidushi Dhaka Dhananjay Singh -
Open Access Article
2 - Computational Method for Fractional-Order Stochastic Delay Differential Equations
Behrouz Parsa Moghaddam Zeynab Salamat Mostaghim Elham Alsaddat Hashemi ZadehDynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order s MoreDynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense. The computational method is based on bilinear spline interpolation and finite difference approximation. The convergence order of the proposed method investigated in the mean square norm and the accuracy of proposed scheme is analyzed in the perspective of the mean absolute error and experimental convergence order. The proposed method is considered in determining statistical indicators of Gompertzian and Nicholson models. The fractional stochastic delay Gompertzian equation is modeled for describing the growth process of a cancer and the fractional stochastic delay Nicholson equation is formulated for explaining a population dynamics of the well-known Nicholson blowflies in ecology. Manuscript profile -
Open Access Article
3 - An Effective Computational Approach by Hybrid Functions Operational Matrix for Solving Mixed Kind of the Partial Integro-Differential Equations
yaser rostamiIn the present paper, a new method is introduced for the approximate solution of two-dimensional mixed Volterra-Fredholm Partial integro-differential equations with initial conditions using twodimensional hybrid Bernstein polynomials and Block-Pulse functions. For this MoreIn the present paper, a new method is introduced for the approximate solution of two-dimensional mixed Volterra-Fredholm Partial integro-differential equations with initial conditions using twodimensional hybrid Bernstein polynomials and Block-Pulse functions. For this purpose, an operational matrix of product and integration of the cross-product and differentiation are introduced that essentially of hybrid functions. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations.. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations.. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations. Convergence analysis and some numerical results are presented to illustrate the effectiveness and accuracy of the method. Manuscript profile -
Open Access Article
4 - Solving random inverse heat conduction problems using PSO and genetic algorithms
I. Hossein Zade Shahbolaghi R. Pourgholi H. Dana Mazraeh S.H. TabasiThe main purpose of this paper is to solve an inverse random differential equation problem using evolutionary algorithms. Particle Swarm Algorithm and Genetic Algorithm are two algorithms that are used in this paper. In this paper, we solve the inverse problem by solvin MoreThe main purpose of this paper is to solve an inverse random differential equation problem using evolutionary algorithms. Particle Swarm Algorithm and Genetic Algorithm are two algorithms that are used in this paper. In this paper, we solve the inverse problem by solving the inverse random differential equation using Crank-Nicholson's method. Then, using the particle swarm optimization algorithm and the genetic algorithm, we solve them. The algorithms presented in this article have advantages over other old methods that have been presented so far. Implementing these algorithms is simpler, have less run time and produce better approximation. The numerical results obtained in this paper also show that the solutions obtained for the examples presented in the numerical results section are highly accurate and have less error. All of the algorithms in this paper to obtain the desired numeric results, have been implemented on the Pentium (R) Dual core E5700 processor at 3.00 GHz. Manuscript profile -
Open Access Article
5 - Zernike radial polynomials method for solving nonlinear singular boundary value problems arising in physiology
M.A. Ebadi E.S. Hashemizadeh A.H. Refahi SheikhaniThe aim of this paper is to provide a new numerical method for solving nonlinear singular differential equations that arise in biology problem. These kind of problems appear in various biology problems like oxygen diffusion in red blood cells, distribution of heat sourc MoreThe aim of this paper is to provide a new numerical method for solving nonlinear singular differential equations that arise in biology problem. These kind of problems appear in various biology problems like oxygen diffusion in red blood cells, distribution of heat source in human head and cancer tumor growth and etc. In this paper this equations are solved by a new numerical method by using Zernike radial polynomials. In the proposed method for the first time the operational matrix of derivative for Zernike radial polynomials is derived and by using this operational matrices of derivative of Zernike radial functions the differential equation convert to a system of algebraic equations that can be solved easily. The implementation of this proposed method is simple and attractive. Finally some applied models are presented to compare the results by other method results, and they show the accuracy and efficiency of the presented method. Manuscript profile -
Open Access Article
6 - Numerical Solution and Error Analysis for Linear and Nonlinear Delay Differential Equations
Ebrahim Amini Ali EbadianIn this paper, we obtain the solution of linear and nonlinear delay differential equations in reproducing kernel space. For this purpose, regarding the equation and conditions governing it, a linear operator is defined and subsequently an orthonormal complete system for MoreIn this paper, we obtain the solution of linear and nonlinear delay differential equations in reproducing kernel space. For this purpose, regarding the equation and conditions governing it, a linear operator is defined and subsequently an orthonormal complete system for reproducing kernel space is obtained by using the adjoint operator and reproducing kernel function. Then, the solution of these equations is obtained in the form of a series of the basic functions. Indeed, the analytical solution is represented by infinite series, and the approximate solution is obtained by using an iterative method. As one of the main aims, the convergence analysis and error behavior are discussed for the proposed method. Finally, some numerical examples are studied to demonstrate the validity and applicability of the proposed method. The obtained results of the proposed method are compared with the exact solutions and the earlier works. The outcomes from numerical examples illustrate that the proposed method is very effective and convenient. Manuscript profile -
Open Access Article
7 - The new implicit finite difference scheme for two-sided space-time fractional partial differential equation
Hamid Reza Khodabandehlo Elyas Shivanian Shaaban MostafaeeFractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solv MoreFractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. Stability, consistency, and (therefore) convergence of the method are examined. It is shown that the fractional method based on the shifted Grunwald formula is unconditionally stable. This study concerns both theoretical and numerical aspects, where we deal with the construction and convergence analysis of the discretization schemes. A numerical example is presented and compared with exact solution for its order of convergence./////////Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. Stability, consistency, and (therefore) convergence of the method are examined. It is shown that the fractional method based on the shifted Grunwald formula is unconditionally stable. This study concerns both theoretical and numerical aspects, where we deal with the construction and convergence analysis of the discretization schemes. A numerical example is presented and compared with exact solution for its order of convergence. Manuscript profile -
Open Access Article
8 - Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes
A. Momeni M. KamraniOrdinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in m MoreOrdinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differential equation will be considered. Because for the numerical solution of these equations we need the simulation of stochastic double integrals, we explain the simulation of these integrals in more details. Also one-step and multi steps methods for the solution of affine random ordinary equations (RODEs) which are an important class of RODEs will be considered. The numerical solution of these equations with Wiener and Compound Poisson processes will be established. Two methods for simulation of the double integrals will be explained, and some numerical examples are provided to confirm the theoretical results numerically. Manuscript profile -
Open Access Article
9 - Existence solutions for new p-Laplacian fractional boundary value problem with impulsive effects
N. Nyamoradi A. RazaniFractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chem MoreFractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dynamics of processes in which sudden, discontinuous jumps occur. For the background, theory and applications of impulsive differential equations. There have been many approaches to study the existence of solutions of impulsive fractional differential equations, such as fixed point theory, topological degree theory, upper and lower solutions methods and monotone iterative method. In this paper, we study the existence of solutions for a new class of p-Laplacian fractional boundary value problem with impulsive effects. By using critical point theory and variational methods, we give some new criteria to guarantee that the impulsive problem have infinitely many solutions. Manuscript profile -
Open Access Article
10 - Presentation of two models for the numerical analysis of fractional integro-differential equations and their comparison
M. BehroozifarIn this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then op MoreIn this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractionalderivative method and the Riemann-Liouville fractional integral method. In the both method, a set of linear or nonlinear algebraic equations are achieved using collocation technique. Tow presented methods are implemented on some test problems. Numerical results explain the high performance of tow methods. Note that all calculations have been done by Mathematica software. Numerical results show that it should be used the first method when the exact solution of differential equation is a polynomial and the second method should be used when the exact solution of differential equation is a transcendental function. Manuscript profile -
Open Access Article
11 - An efficient iterative method for solving differential equations of fuzzy Bratu type
Bahram AgheliIn this paper, we consider the Brato differential equation, in which the boundary condition values are fuzzy values and the purpose is to calculate the approximate Solution. For this, first, using arithmetic operations on fuzzy data, we convert the Bratu differentia MoreIn this paper, we consider the Brato differential equation, in which the boundary condition values are fuzzy values and the purpose is to calculate the approximate Solution. For this, first, using arithmetic operations on fuzzy data, we convert the Bratu differential equation into three sets of differential equations with exact value, and then, using the Tamimi and Ansari method (TAM), the approximate solution of the differential equation can be calculated. Finaly, two examples to express efficiency and simplicity by finding an approximate solution have been presented. Matmetica software has been used for all calculations and plots. Manuscript profile -
Open Access Article
12 - On the structural properties for the cross product of fuzzy numbers with applications
Robab AlikhaniIn the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to a MoreIn the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. The main advantage is that this product preserves the shape of triangular or trapezoidal fuzzy numbers under multiplication and from computational point of view the cross product is more applicable than the usual product. The above mentioned properties motivate us to use the cross product in applications as a possible alternative of the product obtained by Zadeh's extension Principle. The aim of the present paper is to give an explicit formula for the cross product of triangular fuzzy numbers based on the scalar product of fuzzy numbers and then, explicit formulas for the length of cross product of triangular fuzzy numbers and fuzzy derivative of cross product of triangular fuzzy functions. As an application, we apply the cross product concept for the first order linear fuzzy differential equations with fuzzy variable coefficients and obtain its triangular solutions under generalized differentiability. Finally, some examples are given to illustrate the theoretical results. Manuscript profile -
Open Access Article
13 - A numerical method based on Chelyshkov polynomials for solving fractional integro-differential equations
Reza DehghanIn this paper, Chelyshkov expansion approach is presented for solving Volterra fractional order integro-differential equations with Caputo derivative. By means of the properties of Chelyshkov polynomials and numerical integral formula , the solution of fractional integr MoreIn this paper, Chelyshkov expansion approach is presented for solving Volterra fractional order integro-differential equations with Caputo derivative. By means of the properties of Chelyshkov polynomials and numerical integral formula , the solution of fractional integro-differential equations reduced to the solution of algebraic equations. Then, by solving the system of algebraic equations, the solution of the differential-integral equation is presented as a function in the terms of Chelyshkov polynomials. Accuracy and error analysis have been investigated and since the accuracy of the obtained results for fractional integro-differential equations depends on the number of selected Chelyshkov polynomials therefore, with the increase in the number of Chelyshkov polynomials, we can achieve desirable accuracy step by step. All calculations are done by MATLAB software. Also, the numerical results of based on Chelyshkov polynomials method are compared with the results of some of the available methods for the validity, accuracy and efficiency of the technique. Manuscript profile -
Open Access Article
14 - Analytical solutions of differential equations based on genetic meta-heuristic algorithm and ant colony optimization
Nasser Mikaeilvand Akram Javadi Hassan HosseinzadehMany issues are expressed in terms of various applied sciences such as physics, chemistry, and economics, which are concerned with the examination of variations of one or more variables, by differential equations. The prediction of climate, quantum mechanics, wave propa MoreMany issues are expressed in terms of various applied sciences such as physics, chemistry, and economics, which are concerned with the examination of variations of one or more variables, by differential equations. The prediction of climate, quantum mechanics, wave propagation and dynamics of the stock market is some of these examples, whose quick and accurate solution will have tremendous effects on human life, and therefore several methods have been proposed for solving differential equations.The main objective of this study was to investigate the applicability of the antler colony genetic algorithm to the production of experimental solutions and improve them to produce numerical analytic-numerical solutions of various types of ordinary differential equations. An antler colony optimization algorithm (ACO) has an appropriate algorithm with high convergence accuracy and speed for finding approximate solutions for solving optimization problems using probability function dependent on the amount of residual effect of anti-movement. Genetic algorithm is also an optimization method based on mutated and intersect operators with a wide search area that prevents the algorithm from trapping in the local response. The combination of these two algorithms creates an algorithm with maximum efficiency. Examining various examples in the final section of the article will highlight the speed and accuracy of the proposed method. Manuscript profile -
Open Access Article
15 - A semi-analytic method to solve the oxygen diffusion problem
Mojtaba MoradipourIn this paper, a semi-analytic approach is proposed to solve the oxygen diffusion problem.First, we discretize the partial differential equation of the oxygen diffusion problem in temporal direction using the backward finite difference Euler method. We achieve a sequenc MoreIn this paper, a semi-analytic approach is proposed to solve the oxygen diffusion problem.First, we discretize the partial differential equation of the oxygen diffusion problem in temporal direction using the backward finite difference Euler method. We achieve a sequence of free boundary problems in the form of ordinary differential equations (ODEs) in the spatial direction. The ODEs are then solved analytically and a recursive formula is presented to compute the solutions of the ordinary differential equations. The problems of finding unknown boundaries are reduced to nonlinear algebraic problems. Finally, the nonlinear algebraic problems are solved using the root-finding methods such as the false position method. The method proposed in this paper is easy to implement and a comparison with other numerical methods shows that the proposed approach is very efficient and gives very accurate numerical results.Some tables and figures are included to show the efficiency and effectiveness of the proposed technique. Manuscript profile -
Open Access Article
16 - Solvability of Functional Integral-Differential Equations in the Sobolev space w^{k,infinity}(R^n)
Masoome Hosseini Farahi Mahmoud Hassani Reza AllahyariIn 1930, Kuratowski introduced the concept of measure of noncompactness. Later, Banas and Goebel generalized this concept axiomatically, which is more convenient in applications. The principal application of measures of noncompactness in fixed point theory is contained MoreIn 1930, Kuratowski introduced the concept of measure of noncompactness. Later, Banas and Goebel generalized this concept axiomatically, which is more convenient in applications. The principal application of measures of noncompactness in fixed point theory is contained in the Darbo'sfixed point theorem. This is a tool to investigate the existence and behaviour of solutions of manyclasses of integral equations such as Volterra, Fredholm and Uryson types.The technique of measure of noncompactness is applicable in several branches of nonlinear analysis. In particular, it is a very useful tool for several types of integral and integral-differential equations. In addition, the measure of noncompactness is also used in functional equations, fractional partial differential equations, ordinary and partial differential equations, operator theory and optimal control theory. The purpose of this article is to introduce a new measure of noncompactness in the Sobolev space W^(k,∞) (R^n). The results are obtained to solve integral-differential equations. Finally, by providing an example to show the efficiency of our results. Manuscript profile -
Open Access Article
17 - Numerical solution of fractional model of HIV infection in cells CD4+T
Mohammad Reza Doostar Tayebeh Damercheli Alireza VahidiIn this paper, a hybrid function method based on combination of block-pulse functions and Legendre polynomials is used for solving a fractional model of HIV infection of CD4+ T cells in which fractional derivatives are considered in Caputo sense. Using this method, the MoreIn this paper, a hybrid function method based on combination of block-pulse functions and Legendre polynomials is used for solving a fractional model of HIV infection of CD4+ T cells in which fractional derivatives are considered in Caputo sense. Using this method, the system of fractional ordinary differential equations which is the mathematical model for the fractional model of HIV infection of CD4+T cells, is reduced into a system of algebraic equations. This system can be solved by a numerical method. Also, convergence analysis of the method is studied and an upper bound of the error is obtained. To show efficiency and accuracy the proposed method, a numerical example is simulated and some comparisons and results are reported. In this paper, a hybrid function method based on combination of block-pulse functions and Legendre polynomials is used for solving a fractional model of HIV infection of CD4+ T cells in which fractional derivatives are considered in Caputo sense. Using this method, the system of fractional ordinary differential equations which is the mathematical model for the fractional model of HIV infection of CD4+T cells, is reduced into a system of algebraic equations. This system can be solved by a numerical method. Also, convergence analysis of the method is studied and an upper bound of the error is obtained. To show efficiency and accuracy the proposed method, a numerical example is simulated and some comparisons and results are reported. Manuscript profile -
Open Access Article
18 - Classical Lie symmetry group analysis and exact solutions of the fractional modified (2+1)-dimensional Zakharov-Kuznetsov equation
Mir Sajjad Hashemi Ali Haji Badali Farzaneh AlizadehIn this paper, we consider the classical Lie symmetries of fractional modified Zakharov Kuznetsov (which in this paper we abbreviately show this by the mZK equation) equation. Indeed, Lie symmetries are utilized for solving the nonlinear fractional three-dimensional mZK MoreIn this paper, we consider the classical Lie symmetries of fractional modified Zakharov Kuznetsov (which in this paper we abbreviately show this by the mZK equation) equation. Indeed, Lie symmetries are utilized for solving the nonlinear fractional three-dimensional mZK equation with partial derivatives, and by using the infinitesimal transformations and corresponding invariant solutions, we reduce the underlying equation one dimension less than the original mZK equation, and finally, some of the corresponding exact solutions are extracted.Indeed, Lie groups are geometric powerful tools for analyzing and investigating a wide variety of classes of equations such as ordinary differential equations, partial differential equations, fractional differential equations, and integral and integro differential equations. Invariant solutions and conservation laws that play a very significant and astonishing role in physical science can be obtained by this method. Moreover, various kinds of this method such as classical, non-classical, approximate and et cetera can be extracted by utilized in this field. Manuscript profile -
Open Access Article
19 - Quasi-Analytical Solution of the Painleve Fuzzy Differential Equation
Mohammad Adabi tabar Ali Hosseinzadeh Bahram Agheli Samaneh mohamadzadeh farIn this paper, we consider the first-order Painleve differential equation, which variables and coefficients are real but are known boundary conditions and fuzzy numbers. The goal is to calculate the approximate answer for it. Given the boundary conditions fuzzy, it is o MoreIn this paper, we consider the first-order Painleve differential equation, which variables and coefficients are real but are known boundary conditions and fuzzy numbers. The goal is to calculate the approximate answer for it. Given the boundary conditions fuzzy, it is obvious that the approximate answer function must be a fuzzy function. For this purpose, first, by applying arithmetic on fuzzy data with three components of central index, left ambiguity and right ambiguity, it converts Painleve differential equation into three sets of differential equations (central index, left ambiguity and right ambiguity) with accurate data. do . Then, using the Tammy and Ansari (TAM) method, we calculate the approximate solution of each of the three transformed differential equations and arrive at the fuzzy approximate solution of the Painleve differential equation. Finally, by giving an example, we show the suitability of the method by calculating the error and convergence by finding the approximate solution. Manuscript profile -
Open Access Article
20 - On the stability of unbounded differential equations in fuzzy k-normed spaces via fixed point method
M. Madadi Reza SaadatiFirst, using triangular norms and fuzzy sets, we define fuzzy k - normed spaces and then we study the stability of a class of differential equations. We apply a fixed point theorem to prove our stability results. Radu was the first mathematician who applied the fixed po MoreFirst, using triangular norms and fuzzy sets, we define fuzzy k - normed spaces and then we study the stability of a class of differential equations. We apply a fixed point theorem to prove our stability results. Radu was the first mathematician who applied the fixed point method to prove the stability of functional equations both in normed spaces and random normed spaces. We consider the differential equation υ ʹ (ν ) = Г(ν, υ(ν)),which the related integral equation is υ (ν) = υ (m) - ∫_m^ν Г(τ, υ(τ)) dτ.In this article, by a fuzzy control function, we make stable the pseudo integral equation related to the differential equation. Next, we get an approximation for the pseudo integral equation by using the fixed point method. These results prove‎ Hyers - Ulam - Rassias stability and Hyers - Ulam stability in fuzzy k- normed spaces via fixed point method‎. Manuscript profile -
Open Access Article
21 - Existence of fixed points for generalized α-admissible Geraghty and application to solution of nonlinear differential equations
Babak Mohammadi Vahid Parvaneh Farhan GolkarmaneshRecently, samet et al. introduced an interesting extension of the Banach contraction principle. In this paper, motivated by the main idea of Samet et al., we introduce the concept of α-admissible α-θ-generalized mappings in metric spaces and give and p MoreRecently, samet et al. introduced an interesting extension of the Banach contraction principle. In this paper, motivated by the main idea of Samet et al., we introduce the concept of α-admissible α-θ-generalized mappings in metric spaces and give and prove several theorems of the existence and uniqueness of a fixed point in complete metric spaces for such mappings. The results obtained in this study, generalize many of the results in this field, especially, the results presented by Jleli et al. and the work done by Geraghty. By presenting an example, we show that our results are real generalization of the previous results. Next, we get new results in ordered metric spaces and graphical metric spaces using the concept of α-admissible α-θ-generalized mappings. Finally, we present an application of our obtained results for the existence and uniqueness of the solution of nonlinear first-order ordinal differential equations and periodic boundary value problems. Manuscript profile -
Open Access Article
22 - Estimating the half-life of stock price mean reverting: an application of Stochastic Differential Equations
hadi rahmani fazli ahmad molabahramiIn this paper we use stochastic differential equation for estimating the long run equilibrium of the stock prices, the speed of reverting to the mean of the stock prices and the half-life of the stock prices of the selected firms (about 24 active firms) in Tehran Stock MoreIn this paper we use stochastic differential equation for estimating the long run equilibrium of the stock prices, the speed of reverting to the mean of the stock prices and the half-life of the stock prices of the selected firms (about 24 active firms) in Tehran Stock Exchange. We use the stock price data of the selected firms to see if the stock prices of these firms have Unit roots tests. For firms which their stock prices are stationary, without unit roots, we follow an Ornstein-Uhlenbeck stochastic differential equation to estimate the half-life of the stock returns of the selected firm. For firms which their stock prices have got the unit root, we use Geometric Brownian Motion for estimation. The results show that most of the studied companies have a reversible behavior to a long-term average and a half-life of stock prices is estimated to be from 3 to 30 weeks. The estimation of the half-life of the stock prices of the selected firms will provide valuable information for the investors and other agents active in the stock markets. Manuscript profile -
Open Access Article
23 - An application of fuzzy fractional partial differential equations on heart sound signal denoising
farnoosh karimi Tofigh Allahviranloo Saeed AbbasbandyCardiovascular system is a permanent source of information which incorporate to declaration of Cardiovascular diseases. The existence of available valid data is the main part of any research study. Today, in the field of human life study, experimental data by means of d MoreCardiovascular system is a permanent source of information which incorporate to declaration of Cardiovascular diseases. The existence of available valid data is the main part of any research study. Today, in the field of human life study, experimental data by means of different issues are always deviated from their actual values not only in measurement errors but also it is appeared due to the measuring concept. Composing of heart signal, as a real example of signals, with noise signal causes ambiguity in which classical available methods become disable in correct processing and interpretation of these signals. This paper is focused on proposing an algorithm in signal noise reduction of heart sound signal at pre-processing step. This novel de-noising method of heart sound signal is established on arbitrary order fuzzy partial differential equations. Fuzzification is done due to eliminating of absolute boundaries. The propose algorithm of noise reduction is examined by adding Gaussian white noise to the normal heart sound signal without any noise. De-noising method is implemented after presenting the model concept. Attaining the (FFPDE) filter is including the following steps: the filter matrix is defined after using the backward Euler scheme to discretize the fuzzy differential equation. The results indicated that using of fuzzy fractional partial differential equations was completely effective in de-noising of heart sound signals. Manuscript profile -
Open Access Article
24 - The generalized variational iteration method to solve the fractal partial differential equations
Homa Afraz Alireza Khalili GolmankhanehFractional calculus is a branch of classical mathematics, which deals with the generalization of fractional order derivative and integral operator. Recently, a great deal of research has been carried out on the fractional calculus to study the phenomena associated with MoreFractional calculus is a branch of classical mathematics, which deals with the generalization of fractional order derivative and integral operator. Recently, a great deal of research has been carried out on the fractional calculus to study the phenomena associated with fractal structures and processes. Fractals have a fractional dimension and occur naturally in non-linear and imbalanced phenomena in various forms and contexts. In recent years, various types of derivatives and fractional and fractal calculus have been proposed by many scientists and have been extensively utilized. Measurements are localized in physical processes, and local fractional calculus is a useful tool for solving some type of physical and engineering problems. Gangal studied the local fractional calculus and got the relation between it and the fractals. Using the local fractional calculus and fractal properties, he defined the fractal-alpha calculus on a subset of the real line, which is a simple calculs, useful, structural and algorithmic. In this study, we first describe the fractal-F alpha calculus. Next, we propose The generalized variational iteration method based on the fractal calculus. To show the efficiency of fractal calculus and the new method, we solve several fractal partial differential equations with this method and show that this method is better, easier and more suitable than the two other methods mention the above. Manuscript profile -
Open Access Article
25 - Legendre pseudo-spectral method for solving multi-pantograph delay differential equations
Mohammad Hadi Noori Skandari Mostafa Mahmoudi Javad Vahidi Mehdi GhovatmandDelay differential equations have a wide range of applications in science and engineering. When these equations are nonlinear and complex the exact solution can usually not be calculated. So finding a numerical solution with high precision for these equations is essenti MoreDelay differential equations have a wide range of applications in science and engineering. When these equations are nonlinear and complex the exact solution can usually not be calculated. So finding a numerical solution with high precision for these equations is essential. In this paper we present a numerical method based on the transferred Legendre polynomials to solve multiple pantograph delay differential equations. In this method we use the Legendre-Gauss-Lobato collocation points to discretize the problem and turn the problem into a nonlinear programming problem. From solving this nonlinear programming problem we get an approximate solution for the the main multiple pantograph delay differential equation. We analyse the feasibility of the nonlinear programming problem and the convergence of the obtained approximate solution to the exact solution. In addition by solving several numerical examples and comparing the method with other methodsWe show the efficiency and the capability of the proposed method. Manuscript profile -
Open Access Article
26 - Approximated solution of First order Fuzzy Differential Equations under generalized differentiability
T. Allahviranloo N. Ahmady E. AhmadyIn this research, a numerical method by piecewise approximated method for solving fuzzy differential equations is introduced. In this method, the solution by piecewise fuzzy polynomial is present. The base of this method is using fuzzy Taylor expansion on initial value MoreIn this research, a numerical method by piecewise approximated method for solving fuzzy differential equations is introduced. In this method, the solution by piecewise fuzzy polynomial is present. The base of this method is using fuzzy Taylor expansion on initial value of fuzzy differential equations. The existence, uniqueness and convergence of the approximate solution are investigated. To show the advantage of method, this method is compared with the Euler method that was introduced in [۱], and it is shown this method is more accurate than Euler method for solving fuzzy differential equations under generalized differentiability. Manuscript profile -
Open Access Article
27 - Numerical Solution of fuzzy differential equations of nth-order by Adams-Bashforth method
N. ParandinSo far, many methods have been presented to solve the rst-order di erential equations. But, not many studies have been conducted for numerical solution of high-order fuzzy di erential equations. In this research, First, the equation by reducing time, we transform the rs MoreSo far, many methods have been presented to solve the rst-order di erential equations. But, not many studies have been conducted for numerical solution of high-order fuzzy di erential equations. In this research, First, the equation by reducing time, we transform the rst-order equation. Then we have applied Adams-Bashforth multi-step methods for the initial approximation of one order di erential equations. Finally, we examine the accuracy of method by presenting examples. Manuscript profile -
Open Access Article
28 - Symplectic and symmetric methods for the numerical solution of some mathematical models of celestial objects
A. Abdi S.A. HosseiniIn the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov meth MoreIn the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A-stability and L-stability, they are not suitable for the numerical solution of special classes of problems arising from different research areas, for example the mathematical models of celestial objects which are Hamiltonian systems. Since the solution of such problems has special geometric property such as symplecticity and usually reversibility. Therefore, it is natural to search for numerical methods that share this property. It is the purpose of this paper to design high order symplectic and symmetric methods. Efficiency and accuracy of the constructed methods are confirmed by implementing on well-known Hamiltonian problems of the motions of celestial objects. Manuscript profile -
Open Access Article
29 - A Numerical Method for Solving Fuzzy Differential Equations With Fractional Order
N. Ahmady -
Open Access Article
30 - حل مسائل مقدار اولیه کوشی – اویلر فازی مرتبه دوم تحت مشتق پذیری توسعه یافته
مهران چهلابیدر این مقاله، ما یک کلاس از مسائل مقداراولیه فازی مرتبه دوم که در حالت معمول، به معادلات دیفرانسیل کوشی-اویلر معروف هستند، را مطالعه می کنیم. این کار با مطالعه کردن ساختار تابع جواب در حالت معمول و فراهم کردن فضایی مطلوب از توابع مشتق پذیر توسعه یافته، آغاز می شود. در ا Moreدر این مقاله، ما یک کلاس از مسائل مقداراولیه فازی مرتبه دوم که در حالت معمول، به معادلات دیفرانسیل کوشی-اویلر معروف هستند، را مطالعه می کنیم. این کار با مطالعه کردن ساختار تابع جواب در حالت معمول و فراهم کردن فضایی مطلوب از توابع مشتق پذیر توسعه یافته، آغاز می شود. در ادامه، فرایند تولید و ساخت فرمول های جواب همراه با جزئیات بحث شده است. در نهایت، بوسیله حل چند مثال، فرمول های یافت شده، مورد استفاده قرار گرفته و تشریح شده اند. Manuscript profile -
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31 - An Efficient Numerical Algorithm For Solving Linear Differential Equations of Arbitrary Order And Coefficients
S. Hatamzadeh-Varmazyar Z. Masouri -
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32 - A Fuzzy Power Series Method for Solving Fuzzy Differential Equations With Fractional Order
E. Ahmady -
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33 - The Combined Reproducing Kernel Method and Taylor Series for Handling Fractional Differential Equations
A. Alvandi M. Paripour -
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34 - حل معادلات دیفرانسیل ماتریسی خطی مرتبه اول با استفاده از رویکرد ماتریس برنشتاین
زهرا لرکوجوری ناصر میکائیل وند اسماعیل بابلیاندر این مقاله از یک چارچوب جدید برای حل یک رده از معادلات دیفرانسیل ماتریسی خطی استفاده شده است. برای انجام این کار، ماتریس عملیاتی مشتق مبتنی بر چند جمله ای برنشتاین انتقال یافته همراه با روش همبستگی برای کاهش مسئله اصلی به دستگاه معادلات ماتریس خطی مورد بهره برداری قرا Moreدر این مقاله از یک چارچوب جدید برای حل یک رده از معادلات دیفرانسیل ماتریسی خطی استفاده شده است. برای انجام این کار، ماتریس عملیاتی مشتق مبتنی بر چند جمله ای برنشتاین انتقال یافته همراه با روش همبستگی برای کاهش مسئله اصلی به دستگاه معادلات ماتریس خطی مورد بهره برداری قرار می گیرد. تخمین خطای این روش ارائه شده است. آزمایش­های عددی برای نمایش کاربرد و کارایی روش ارائه شده است. Manuscript profile -
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35 - A Numerical Method For Solving Physiology Problems By Shifted Chebyshev Operational Matrix
E. Hashemizadeh F. Mahmoodi -
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36 - Application of Laguerre Polynomials for Solving Infinite Boundary Integro-Differential Equations
A. Riahifar M. Matinfar -
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37 - The Use of Fuzzy Variational Iteration Method For Solving Second-Order Fuzzy Abel-Volterra Integro-Differential Equations
S. Sadigh Behzadi -
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38 - Bernstein Multi-Scaling Operational Matrix Method for Nonlinear Matrix Differential Models of Second-Order
M. Mohamadi E. Babolian S. A. Yousefi -
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39 - Nonlinear Fuzzy Volterra Integro-differential Equation of N-th Order: Analytic Solution and Existence and Uniqueness of Solution
L. Hooshangian -
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40 - وجود جوابهای ضعیف برای یک سیستم مقدار مرزی فراکشنالی نیمه-خطی ولترا – فردهلم
الیاس شیوانیاناین مقاله به مطالعه جوابهای های ضعیف یک رده از سیستم غیر خطی از مسایل مقدار مرزی کسری شامل ترم های انتگرال خطی ولترا و فردهلم می پردازد. این سیستم معادلات انتگرال-دیفرانسیل نیمه خطی کسری ولترا-فردهلم همچنین دارای یک ترم گرادیان از یک جمله غیر خطی هست. ما تئوری نقطه بحرا Moreاین مقاله به مطالعه جوابهای های ضعیف یک رده از سیستم غیر خطی از مسایل مقدار مرزی کسری شامل ترم های انتگرال خطی ولترا و فردهلم می پردازد. این سیستم معادلات انتگرال-دیفرانسیل نیمه خطی کسری ولترا-فردهلم همچنین دارای یک ترم گرادیان از یک جمله غیر خطی هست. ما تئوری نقطه بحرانی و ساختار تغییراتی را برای اثبات وجود حداقل سه جواب ضعیف مجزا برای سیستم اعمال می کنیم. برای این منظور، ما از قضیه معروفی درباره ساخت مجموعه نقاط بحرانی از تابعکها با شرط فشردگی ضعیف بهره می بریم. علاوه بر این، مثالی برای تأیید آنالیز و کاربرد نظریه ارائه شده، آورده شده است. Manuscript profile -
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41 - کنترل بازخورد بهینه معادلات انتگرو-دیفرانسیل شبه خطی کسری در فضاهای باناخ
سهراب ولی زاده عبدالله برهانی فر محمد رضا عبدالله پوراخیرا، پیشرفت قابل توجهی در وجود جوابهای خفیف معادلات انتگرو-دیفرانسیل شبه خطی کسری صورت گرفته است ولی کنترل بهینه ارائه نشده است. هدف این مقاله، بررسی کنترل بازخورد بهینه معادلات انتگرو-دیفرانسیل شبه خطی کسری در یک فضای دلخواه باناخ مجهز به عملگرهای نیم گروه فشرده گستر Moreاخیرا، پیشرفت قابل توجهی در وجود جوابهای خفیف معادلات انتگرو-دیفرانسیل شبه خطی کسری صورت گرفته است ولی کنترل بهینه ارائه نشده است. هدف این مقاله، بررسی کنترل بازخورد بهینه معادلات انتگرو-دیفرانسیل شبه خطی کسری در یک فضای دلخواه باناخ مجهز به عملگرهای نیم گروه فشرده گسترش یافته است. Manuscript profile -
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42 - Contrast of Homotopy and Adomian Decomposition Methods with Mittage-Leffler Function for Solving Some Nonlinear Fractional Partial Differential Equations
M. Jahanshahi H. Kazemi demneh -
Open Access Article
43 - حل معادلات انتگرال ولترای نوع دوم با هسته پیچشی
محمد صادق باریکبین علیرضا وحیدی طیبه دمیرچلیدر این مقاله، یک روش تقریبی برای حل معادلات انتگرال ولترای نوع دوم ارائه می­دهیم. این روش بر مبنای روش بسط تیلوری است که مالک نژاد و آقازاده برای بدست آوردن جواب تقریبی معادلات انتگرال ولترای نوع دوم با هسته پیچشی و مالک نژاد و دمرچلی جهت یافتن جواب تقریبی دستگاه مع Moreدر این مقاله، یک روش تقریبی برای حل معادلات انتگرال ولترای نوع دوم ارائه می­دهیم. این روش بر مبنای روش بسط تیلوری است که مالک نژاد و آقازاده برای بدست آوردن جواب تقریبی معادلات انتگرال ولترای نوع دوم با هسته پیچشی و مالک نژاد و دمرچلی جهت یافتن جواب تقریبی دستگاه معادلات انتگرال ولترای نوع دوم به کار بسته­اند. روش بسط تیلور، معادله انتگرال را به یک دستگاه معادلات دیفرانسیل معمولی خطی تبدیل می­کند که در این حالت شرایط مرزی مشخص مورد نیاز است. شرایط مرزی می­تواند با استفاده از تکنیک انتگرالگیری به جای تکنیک مشتقگیری بدست آید. روش ارائه شده پایدارتر از روش مشتقگیری است و می­تواند جهت یافتن جواب تقریبی معادله انتگرال ولترا با هسته­های هموار و منفرد ضعیف استفاده شود. تحلیل خطای روش نیز ارائه شده است. مقایسه بین نتایج بدست آمده ما و نتایج قبلی نشان می­دهد که روش پیشنهادی دقیق­تر و پایدارتر است. Manuscript profile -
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44 - یک روش مستقیم برای حل معادلات دیفرانسیل تاخیری خطی
E. Zeynal E. Babolian T. Damercheliدر این مقاله، روشهای مستقیم برای حل معادلات دیفرانسیل تاخیری خطی براساس شکل برداری توابع بلاک پالس و توابع مثلثی پیشنهاد شده است. سپس از ماتریس عملیاتی انتگرال گیری توابع بلاک پالس و توابع مثلثی، برای تبدیل معادلات دیفرانسیل تاخیری خطی به یک دستگاه معادلات جبری اس Moreدر این مقاله، روشهای مستقیم برای حل معادلات دیفرانسیل تاخیری خطی براساس شکل برداری توابع بلاک پالس و توابع مثلثی پیشنهاد شده است. سپس از ماتریس عملیاتی انتگرال گیری توابع بلاک پالس و توابع مثلثی، برای تبدیل معادلات دیفرانسیل تاخیری خطی به یک دستگاه معادلات جبری استفاده شده است. بعلاوه برای نشان دادن قابلیت و دقت این روش ها چند مثال ارائه شده است. همچنین تجزیه و تحلیل همگرایی این روش ها بحث شده است. Manuscript profile -
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45 - یک روش عددی برای حل معادله دیفرانسیل ضربه فازی براساس روشهای فازی
محدثه دیرباز سعید عباسبندیدر این مقاله، ابتدا روش درونیابی تفضلات تقسیم شدهی نیوتن بر اساس تفاضلات تقسیمشدهی هاکوهارا، برای دادههای فازی معرفی میشود. سپس روشهای عددی اویلر فازی و اویلر بهبودیافته فازی برای حل مسئله مقدار اولیه ضربه فازی به کار میروند. بهعلاوه، الگوریتم برای حل مسئله مق Moreدر این مقاله، ابتدا روش درونیابی تفضلات تقسیم شدهی نیوتن بر اساس تفاضلات تقسیمشدهی هاکوهارا، برای دادههای فازی معرفی میشود. سپس روشهای عددی اویلر فازی و اویلر بهبودیافته فازی برای حل مسئله مقدار اولیه ضربه فازی به کار میروند. بهعلاوه، الگوریتم برای حل مسئله مقدار اولیه ضربه فازی توضیح داده میشود و خطای قطع شدهی موضعی آنها با جزئیات محاسبه میشود. در نهایت، برای نشان دادن کارآمدی روش چند مثال عددی حل میشود. Manuscript profile -
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46 - روش عددی صریح برای سیستمهای دینامیک غیرموضعی با تأخیردر زمان بر پایه درونیابی اسپلاین مربعی
حسن پنج مینی بهروز پارسا مقدم الهام هاشمی زادهدر این مقاله، روشی صریح برای حل عددی معادلات دیفرانسیل غیرموضعی با تأخیر در زمان ارائه و مورد بررسی قرار می گیرد. در روش ارائه شده، درونیابی اسپلاین مربعی بکار گرفته شده است و خطای روش ارائه شده آنالیز گردیده است. کارایی و اعتبار روش پیشنهادی در مدلهای آیکدا و هاتچینسو Moreدر این مقاله، روشی صریح برای حل عددی معادلات دیفرانسیل غیرموضعی با تأخیر در زمان ارائه و مورد بررسی قرار می گیرد. در روش ارائه شده، درونیابی اسپلاین مربعی بکار گرفته شده است و خطای روش ارائه شده آنالیز گردیده است. کارایی و اعتبار روش پیشنهادی در مدلهای آیکدا و هاتچینسون غیرموضعی تأخیری با استناد مفاهیم خطا و همگرایی روشهای عددی به ازای مقادیر مختلف پارامترهای مرتبه کسری نمایان شده است. Manuscript profile -
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47 - Application of Variational Calculus to Integrability of Differential Equations with Physical Applications
Mehmet Pakdemirli -
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48 - جواب عددی از معادلات دیفرانسیل فازی هیبریدی مرتبه دوم با دیفرانسیل پذیری تعمیم یافته
نیره شهریاری سعید عباسبندیدر این مقاله، یک روش عددی برای حل معادلات دیفرانسیل فازی هیبریدی مرتبه دوم با استفاده از بسط تیلور فازی تحت دیفرانسیل پذیری تعمیم یافته هاکوهارا و همچنین قضیه همگرایی ارائه شده است. همچنین کاربرد روش با حل چندین مثال عددی نشان داده شده است. نتایج نهایی نشان دهنده& Moreدر این مقاله، یک روش عددی برای حل معادلات دیفرانسیل فازی هیبریدی مرتبه دوم با استفاده از بسط تیلور فازی تحت دیفرانسیل پذیری تعمیم یافته هاکوهارا و همچنین قضیه همگرایی ارائه شده است. همچنین کاربرد روش با حل چندین مثال عددی نشان داده شده است. نتایج نهایی نشان دهنده جواب معادلات دیفرانسیل فازی هیبریدی مرتبه دوم است. Manuscript profile -
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49 - یک روش عددی سریع براساس توابع ترکیبی تیلور و بلاک پالس برای حل معادلات دیفراسیل تاخیری
مهدی ابلاغی علیرضا وحیدی اسماعیل بابلیاندر این مقاله، یک روش عددی سریع برای یافتن جواب معادلات دیفرانسیل تأخیری غیر خطی با استفاده از توابع ترکیبی چند جمله های تیلور و بلاک پالس پیشنهاد شده است. در ابتدا، برخی از ویژگیهای توابع ترکیبی بلاک پالس و چند جمله های تیلور در فاصله (0,1] معرفی می شوند. در این روش طیف Moreدر این مقاله، یک روش عددی سریع برای یافتن جواب معادلات دیفرانسیل تأخیری غیر خطی با استفاده از توابع ترکیبی چند جمله های تیلور و بلاک پالس پیشنهاد شده است. در ابتدا، برخی از ویژگیهای توابع ترکیبی بلاک پالس و چند جمله های تیلور در فاصله (0,1] معرفی می شوند. در این روش طیفی، ماتریس های عملیاتی مشتق، انتگرال و ضرایب ماتریس محاسبه و استفاده می شوند. بر اساس این توابع قطعه ای ، معادلات دیفرانسیل تاخیری را به دستگاه معادلات جبری خطی یا غیر خطی تبدیل می کنیم. همچنین، آنالیز و تحلیل خطا برای روش نیز ارائه شده است. در انتها ، مثالهای عددی نشان می دهند روش پیشنهادی جدید در مقایسه با سایر روشهای دیگر از دقت و کارایی بالایی برخوردار است. Manuscript profile -
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50 - یک روش ماتریس-عملیاتی ژاکوبی انتقال یافته جدید برای حل معادله دیفرانسیل مرتبه متغیر کسری غیرخطی با تاخیرهای متناسب
حمید خدابنده لو الیاس شیوانیان سعید عباسبندیدر این کار، معادله دیفرانسیل مرتبه متغیر کسری چند جمله ای غیرخطی تعمیم یافته با تاخیرهای متناسب ارائه می شود. یک تکنیک ماتریس عملیاتی ژاکوبی جدید برای حل یک رده از این معادلات معرفی می شود، به طوری که مساله اصلی تبدیل به سیستم معادلات جبری می شود که می توانیم آن را به ص Moreدر این کار، معادله دیفرانسیل مرتبه متغیر کسری چند جمله ای غیرخطی تعمیم یافته با تاخیرهای متناسب ارائه می شود. یک تکنیک ماتریس عملیاتی ژاکوبی جدید برای حل یک رده از این معادلات معرفی می شود، به طوری که مساله اصلی تبدیل به سیستم معادلات جبری می شود که می توانیم آن را به صورت عددی حل کنیم. تکنیک پیشنهادی با موفقیت برای مساله فوق الذکر توسعه یافته است. تست های عددی جامعی برای نشان دادن کلیت، کارایی، دقت روش ارائه شده و انعطاف پذیری این تکنیک بررسی و تایید می گردد. آزمایشهای عددی آن را با روشهای موجود دیگر مانند روش بازتولید هسته هیلبرت (RKHSM) مقایسه می کنیم. مقایسه نتایج این روش ها و همچنین مقایسه روش فعلی (NSJOM) با جواب واقعی، نشان دهنده اعتبار و کارایی این تکنیک است. بررسی ها نشان می دهد که اجرای این روش آسان است و این تکنیک به عنوان تعمیم بسیاری از روشهای عددی در نظر گرفته می شود. علاوه بر این، خطا و کران آن برآورد می شود. Manuscript profile -
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51 - یک روش تکراری جدید برای حل معادلات انتگرال دیفرانسیل ولترا-فردهولم
احمد جعفریانمعادلات انتگرال دیفرانسیل دارای کاربردهای بسیار وسیعی در زمینه های مختلف علمی از جمله فیزیک وبیولوزی دارند. در این مقاله یک روش تکرار شونده جدیدبرای حل معادلات انتگرال دیفرانسیل ولترا-فردهولم برای اولین بار ارایه می شود. روش با جزییات توضیح داده خواهد شد و با حل چند مثا Moreمعادلات انتگرال دیفرانسیل دارای کاربردهای بسیار وسیعی در زمینه های مختلف علمی از جمله فیزیک وبیولوزی دارند. در این مقاله یک روش تکرار شونده جدیدبرای حل معادلات انتگرال دیفرانسیل ولترا-فردهولم برای اولین بار ارایه می شود. روش با جزییات توضیح داده خواهد شد و با حل چند مثال کارایی آن بررسی می شود. روش تکراری جدید به مانند یک فرمول بازگشتی عمل می کند. برای نشان دادن کارایی روش نتایج حل مسایل با جواب دقیق مقایسه می شود. نتایج به دست آمده از کارایی روش ما حکایت دارد. Manuscript profile -
Open Access Article
52 - Solution of fuzzy differential equations
M. Otadi M. Mosleh -
Open Access Article
53 - Approximate Solution of Fuzzy Fractional Differential Equations
A. Panahi -
Open Access Article
54 - A Piecewise Approximate Method for Solving Second Order Fuzzy Differential Equations Under Generalized Differentiability
E. Ahmady N. Ahmady -
Open Access Article
55 - Study on usage of Elzaki transform for the ordinary differential equations with non-constant coefficients
M. Eslaminasab S. Abbasbandy -
Open Access Article
56 - Generalized H-differentiability for solving second order linear fuzzy differential equations
P. Darabi S. Moloudzadeh‎ H. Khandani‎ -
Open Access Article
57 - Partial Differential Equations applied to Medical Image Segmentation
B. Bagheri R. Ezzati -
Open Access Article
58 - Modified homotopy perturbation method for solving non-linear oscillator's equations
A. R. Vahidi Z. Azimzadeh M. Shahrestani‎ -
Open Access Article
59 - Numerical solution of nonlinear fractional pantograph differential equations with boundary conditions using Jacobi polynomials
Somayeh Nemati Faezeh BakoueiIn this research, we have numerically solved a set of nonlinear fractional pantograph differential equations with boundary conditions using Jacobi polynomials. The present method turns the problem into a system of nonlinear algebraic equations, which simplifies the prob MoreIn this research, we have numerically solved a set of nonlinear fractional pantograph differential equations with boundary conditions using Jacobi polynomials. The present method turns the problem into a system of nonlinear algebraic equations, which simplifies the problem. It is suggested to use Jacobi wavelets to solve such problems, because in problems where the solution is not smooth enough, using wavelets by keeping the polynomial degree constant and increasing the number of wavelets will lead to an improvement in the approximation. Manuscript profile -
Open Access Article
60 - An Interval Parametric Approach for the Solution of One Dimensional Generalized Thermoelastic Problem
S Mandal S Pal Sarkar T Kumar Roy -
Open Access Article
61 - A Mathematical Formulation to Estimate the Fundamental Period of High-Rise Buildings Including Flexural-Shear Behavior and Structural Interaction
E Noroozinejad Farsangi H Melatdoust A Bin Adnan -
Open Access Article
62 - 3D Thermoelastic Interactions in an Anisotropic Lastic Slab Due to Prescribed Surface Temparature
Gh Debkumar L Abhijit R Kumar R Surath -
Open Access Article
63 - Numerical Solution of fuzzy differential equations of nth-order by Adams-Moulton method
نورالدین پرندین -
Open Access Article
64 - Using finite difference method for solving linear two-point fuzzy boundary value problems based on extension principle
Seyed Majid Alavi -
Open Access Article
65 - A Second-Order Accurate Numerical Approximation for Two-Sided Fractional Boundary Value Advection-Diffusion Problem
Elyas Shivanian Hamid Reza Khodabandehlo -
Open Access Article
66 - The existence and uniqueness of the solution for uncertain functional differential equations
Nazanin Ahmadi Samira Siahmansouri -
Open Access Article
67 - A new reproducing kernel method for solving Volterra integro-di erential equations
Razieh Ketabchi -
Open Access Article
68 - An approximate method for solving fractional system differential equations
Mohammad Adabitabar Firozja Bahram Agheli -
Open Access Article
69 - Application of semi-analytic method to compute the moments for solution of logistic model
MohammadAli Jafari -
Open Access Article
70 - Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations
Khalid Aboodh -
Open Access Article
71 - A new technique for solving Fredholm integro-differential equations using the reproducing kernel method
Razieh Ketabchi -
Open Access Article
72 - A novel existence and uniqueness theorem for solutions to FDEs driven by Lius process with weak Lipschitz coefficients
S. Siah-Mansouri O. Solaymani Fard M. M. Gachpazan -
Open Access Article
73 - General Solution for Fuzzy Linear Second Order Differential Equation Using First Solution
Laleh Hooshangian -
Open Access Article
74 - Confidence Interval for Solutions of the Black-Scholes Model
Mehran Paziresh Mohamad Ali Jafari Majid Feshari -
Open Access Article
75 - Analytical and numerical solutions for the pricing of a combination of two financial derivatives in a market under Hull-White model
Hossein Sahebi Fard Elham Dastranj Abdolmajid Abdolbaghi Ataabadi -
Open Access Article
76 - Optimization of estimates and comparison of their efficiency under stochastic methods and its application in financial models
Kianoush Fathi vajargah Hamid Mottaghi Golshan Abbas Arjomandfar -
Open Access Article
77 - An Uncertain Renewal Stock Model for Barrier Options Pricing with Floating Interest Rate
Behzad Abbasi Kazem NouriOption pricing is a main topic in contemporary financial theories, captivating the attention of numerous financial analysts and economists. Barrier option, classified as an exotic option, derives its value from the behavior of an underlying asset. The outcome of this o MoreOption pricing is a main topic in contemporary financial theories, captivating the attention of numerous financial analysts and economists. Barrier option, classified as an exotic option, derives its value from the behavior of an underlying asset. The outcome of this option is based on whether or not the price of the underlying asset has reached a predetermined barrier level. Over the years, the stock price has been represented through continuous stochastic processes, with the prominent one being the Brownian motion process. Correspondingly, the widely used Black-Scholes model has been employed. Nevertheless, it has become evident that utilizing stochastic differential equations to characterize the stock price process is unsuitable and leads to a perplexing paradox. As a result, many researchers have turned to incorporating fuzzy or uncertain environments in such situations. This study presents a methodology for pricing barrier options on stocks in an uncertain environment, in which the interarrival times are uncertain variables. The approach employs the Liu process and renewal uncertain process, considering the interest rate as dynamic and floating. The pricing formulas for knock-in barrier options are derived using α-paths of uncertain differential equations with jumps. Manuscript profile -
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78 - Solving linear and nonlinear optimal control problem using modified adomian decomposition method
Ahmad Fakharian Mohammad Taghi Hamidi Beheshti -
Open Access Article
79 - Derivation of Equation of Motion for the Pillow-Shape Seismic Base Isolation System
Ali Tayaran Mahmood Hosseini -
Open Access Article
80 - Task-space Control of Electrically Driven Robots
Morteza Tavakoli -
Open Access Article
81 - Numerical Simulation and Methodology Based on Improved Split Step Method for Studying Stochastic Models
Leila Torkzadeh Hassan Ranjbar -
Open Access Article
82 - اسـتفاده از تجزیـه و تحلیـل تقـارن لـی بـرای معـادلات دیفرانسـیل جزئـی مرتبـه دوم
موسی ایلی جعفر بی آزار زینب آیتیبـه دسـت آوردن راه حـل تحلیلـی یا عددی معادلات دیفرانسـیل کسـری بـه ویژه در سـال هـای اخیر ،یکی از مسـائل مشـکل و چالـش برانگیز در میـان ریاضیدانان و مهندسـان اسـت.هدف از ایـن مقالـه توسـعه روش تقـارن لی برای حـل معادلات دیفرانسـیل جزئی مرتبه دوم بر اسـاس مشـتق کسـری قا Moreبـه دسـت آوردن راه حـل تحلیلـی یا عددی معادلات دیفرانسـیل کسـری بـه ویژه در سـال هـای اخیر ،یکی از مسـائل مشـکل و چالـش برانگیز در میـان ریاضیدانان و مهندسـان اسـت.هدف از ایـن مقالـه توسـعه روش تقـارن لی برای حـل معادلات دیفرانسـیل جزئی مرتبه دوم بر اسـاس مشـتق کسـری قابل انطباق اسـت. برخی از نمونـه هـای عددی برای نشـان دادن رویکرد پیشـنهادی ارائه شـده اسـت. Manuscript profile -
Open Access Article
83 - بهینه سازی معادلات دیفرانسیل خنثی با استفاده از روش MHAM و RSK
شادان صدیق بهزادیدر این مقاله، یک معادله دیفرانسیل خام غیرخطی با استفاده از روش تکراری Rosenbrock، روش تحلیلی Homotype و روش سری قدرت حل شده است. حل تقریبی این معادله در قالب مجموعه ای محاسبه می شود که اجزای آن با استفاده از روابط بازگشتی محاسبه می شوند. برخی از نمونه های عددی برای نشان Moreدر این مقاله، یک معادله دیفرانسیل خام غیرخطی با استفاده از روش تکراری Rosenbrock، روش تحلیلی Homotype و روش سری قدرت حل شده است. حل تقریبی این معادله در قالب مجموعه ای محاسبه می شود که اجزای آن با استفاده از روابط بازگشتی محاسبه می شوند. برخی از نمونه های عددی برای نشان دادن دقت روش های ارائه شده مورد مطالعه قرار می گیرند. Manuscript profile -
Open Access Article
84 - Shifted Chebyshev approach for the solution of delay Fredholm and Volterra integro-differential equations via perturbed Galerkin method
Kazeem Issa Jafar Biazar Babatunde Yisa -
Open Access Article
85 - حل عددی معادلات دیفرانسیل کسری زمانی فوکر-پلانک -کولموگروف با استفاده از روش موجک هار و بررسی همگرایی و خطا
شعبان محمدی S. Reza Hejaziهدف از این مقاله ارائه یک روش عددی کارآمد برای یافتن جواب های عددی معادلات دیفرانسیل کسری-زمانی فوکر-پلانک-کلموگروف است. موج هار اولین بار بود که معرفی شد. معادله دیفرانسیل کسری زمان فوکر-پلانک-کلموگروف با استفاده از ماتریس عملیات موجک هار در این تکنیک به معادله خطی تبد Moreهدف از این مقاله ارائه یک روش عددی کارآمد برای یافتن جواب های عددی معادلات دیفرانسیل کسری-زمانی فوکر-پلانک-کلموگروف است. موج هار اولین بار بود که معرفی شد. معادله دیفرانسیل کسری زمان فوکر-پلانک-کلموگروف با استفاده از ماتریس عملیات موجک هار در این تکنیک به معادله خطی تبدیل می شود. این روش این مزیت را دارد که حل آن ساده است. شبیه سازی با استفاده از نرم افزار MATLAB انجام شده است. در نهایت، استراتژی پیشنهادی برای حل مشکلات خاص مورد استفاده قرار گرفت. نتایج نشان داد که روش عددی پیشنهادی هنگام استفاده از معادلات دیفرانسیل کسر زمانی فوکر-پلانک-کلموگروف بسیار دقیق و موثر است. نتایج برخی از مثالهای عددی به صورت جدول و نمودار مستند شده است تا کارایی و دقت روش پیشنهادی را توضیح دهد. علاوه بر این، برای همگرایی تکنیک پیشنهادی، نابرابری در زمینه تحلیل خطا به دست میآید Manuscript profile -
Open Access Article
86 - تقارنهای لی ، خود الحاقی و قوانین بقا معادله مونج آمپر
زهرا مومن نژاد مهدی نجفی خواهاین مقاله معادله دو بعدی بسط یافته مونج آمپر را با روش لی بررسی میکند. تقارنهای لس معادله مونج آمپر یافته شدند و روش خود الحاقی غیر خطی برای این معادله در نظر گرفته شده است. با بکارگیری روش ابراگیموف و عملگرهای نوتر، مجموعه بی نهایتی از قوانین پایستگی وابسته به تقارنهای Moreاین مقاله معادله دو بعدی بسط یافته مونج آمپر را با روش لی بررسی میکند. تقارنهای لس معادله مونج آمپر یافته شدند و روش خود الحاقی غیر خطی برای این معادله در نظر گرفته شده است. با بکارگیری روش ابراگیموف و عملگرهای نوتر، مجموعه بی نهایتی از قوانین پایستگی وابسته به تقارنهای لی معادله مونج-آمپر استخراج میشوند. مقادیر بقا متناظر از چگالی های مربوطه به ترتیب محاسبه شده اند. Manuscript profile -
Open Access Article
87 - SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS UNDER GENERALIZED DIFFERENTIABILITY BY ADOMIAN DECOMPOSITION METHOD
ت. اللهویرانلو ل. جمشیدی -
Open Access Article
88 - A NOTE ON THE AVERAGING METHOD FOR DIFFERENTIAL EQUATIONS WITH MAXIMA
Victor Plotnikov Olga Kichmarenko -
Open Access Article
89 - COMPARING NUMERICAL METHODS FOR THE SOLUTION OF THE DAMPED FORCED OSCILLATOR PROBLEM
ع.ر وحیدی ق. اسدی کردشولی ز. عظیم زاده -
Open Access Article
90 - SOLVING NONLINEAR KLEIN-GORDON EQUATION WITH A QUADRATIC NONLINEAR TERM USING HOMOTOPY ANALYSIS METHOD
H. جعفری م. سعیدی م. عرب فیروزجایی -
Open Access Article
91 - APPLICATION OF EXP-FUNCTION METHOD TO THE (2+1)-DIMENSIONAL CALOGERO BOGOYAVLANSKII SCHIFF EQUATION
Z. آیتی ج. بی آزار -
Open Access Article
92 - Analytic-Approximate Solution For An Integro- Differential Equation Arising In Oscillating Magnetic Fields Using Homotopy Analysis Method
H. صابری نیک S. عفتی ر. بوژآبادی -
Open Access Article
93 - Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant
Anil Kr. Aggarwal Sanjeev Kumar Vikram Singh Tarun Kr. Garg -
Open Access Article
94 - Investigating and Improving the Uncertainty of Control Systems Using Fuzzy Differential Equations
Fateme Arab -
Open Access Article
95 - Modeling of Gold coin futures with stochastic differential equations
Rahele Baqeri mohammadreza setayesh Reza RadfarThe capital market is one of the financial markets that in a dynamic economy can pave the way for long-term economic growth.Futures contracts that derive their values from an underlying asset, are included these financial instruments.To enter the futures market, the inv MoreThe capital market is one of the financial markets that in a dynamic economy can pave the way for long-term economic growth.Futures contracts that derive their values from an underlying asset, are included these financial instruments.To enter the futures market, the investor needs to anticipate future trends to cover his risk. For this purpose, the appropriate random differential equation has been selected to model the prediction of future coin contracts in the present study.Thus, after providing the necessary explanations about the necessity of using random models and as a result of new principles called random accounts, to introduce the most important stochastic differential equation in financial sciences including geometric Brownian, geometric Brownian with jump term, Heston and the explained model are discussed. Then, the appropriate model is selected, with a practical approach and based on the ability of each model to predict the price of futures contracts by assembling the Monte Carlo.The results of the fitness criteria regarding the predictive power indicate the superiority of the model explained in these contracts. Manuscript profile -
Open Access Article
96 - Comparison of the performance of Merton and Heston models in predicting the price of gold coin futures contracts
Rahele Baqeri mohammadreza setayeshToday, investing in gold markets is an important part of any country's economy, so estimating the price of gold is one of the most important topics of study for economists and financial analysts who have developed different approaches and perspectives. Naturally, method MoreToday, investing in gold markets is an important part of any country's economy, so estimating the price of gold is one of the most important topics of study for economists and financial analysts who have developed different approaches and perspectives. Naturally, methods can be durable and suitable for use that have the least investment error and risk. In developing countries such as Iran, due to inflation and uncertainty about the future, the demand for gold to cover the risk of inflation is high.The formation of the Bahar Azadi coin futures contract market in the Commodity Exchange in recent years has also helped to create an organized market to cover risk and also to use arbitrage opportunities in the gold market. The trading statistics of Bahar Azadi coin futures contract have grown significantly since the entry of its first symbol in the trading table of Iran Commodity Exchange, so that it has created an organized market with high trading volume and appropriate liquidity in the field of derivatives trading in the country. In this study, we decided to use two models of stochastic differential equations (Heston and Merton) to predict the price of futures contracts and compare the results. Manuscript profile -
Open Access Article
97 - Estimation of Value at Risk with Extreme Value Theory approach and using Stochastic Differential Equation
Amir Shafiee reza raei Hossein Abdoh Tabrizi saeed falahporThe occurrence of financial crises in recent decades has caused a lot of damage to the economy as well as economic enterprises in many countries. The Extreme Value Approach is a new approach to the phenomenon of financial crisis, which has been able to analyze the event MoreThe occurrence of financial crises in recent decades has caused a lot of damage to the economy as well as economic enterprises in many countries. The Extreme Value Approach is a new approach to the phenomenon of financial crisis, which has been able to analyze the events that are less likely to occur but the damage caused by them is significant. In this study, we use the Extreme Value theory and Stochastic differential equations to find a new method for estimating the more precisely the value at risk. For this purpose, after estimating the parameters of the Stochastic differential equations, which includes the geometric Brownian motion, the geometric Brownian motion with the jump, the nonlinear GARCH model, and the Heston model, simulate the Monte Carlo simulations of future paths and then use peak over threshold approach, to estimate the value We at risk. The results of the simultaneous use of Stochastic differential equations and Extreme value theory are compared with historical simulations and variance-covariance approaches for value at risk. The results of Back-test techniques on value at risk indicate the superiority of the Heston model in estimation of value at risk. Manuscript profile -
Open Access Article
98 - Analytical-Approximate Solution for Nonlinear Volterra Integro-Differential Equations
M. Matinfar A. Riahifar -
Open Access Article
99 - Initial value problems for second order hybrid fuzzy differential equations
M. Otadi -
Open Access Article
100 - Application of DJ method to Ito stochastic differential equations
H. Deilami Azodi -
Open Access Article
101 - A Chebyshev functions method for solving linear and nonlinear fractional differential equations based on Hilfer fractional derivative
M. H. Derakhshan A. Aminataei -
Open Access Article
102 - The moving frame method and invariant subspace under parametric group actions
Y. Alipour Fakhri Y. Azadi -
Open Access Article
103 - Solvability of infinite systems of differential equations of general order in the sequence space $bv_{\infty}$
M. H. Saboori M. Hassani R. AllahyariWe introduce the Hausdorff measure of noncompactness in the sequence space $bv_{\infty}$ and investigate the existence of solution of infinite systems of differential equations with respect to Hausdorff measure of noncompactness. Finally, we present an example to defend MoreWe introduce the Hausdorff measure of noncompactness in the sequence space $bv_{\infty}$ and investigate the existence of solution of infinite systems of differential equations with respect to Hausdorff measure of noncompactness. Finally, we present an example to defend of theorem of existential. Manuscript profile -
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104 - Homogeneous fuzzy wave equation on the half-line under generalized Hukuhara differentiability
S. Rahimi Charmhini M. S. Asgari -
Open Access Article
105 - A note on the convergence of the Zakharov-Kuznetsov equation by homotopy analysis method
A. Fallahzadeh M. A. Fariborzi Araghi -
Open Access Article
106 - Solving the liner quadratic differential equations with constant coefficients using Taylor series with step size h
M. Karimian -
Open Access Article
107 - Numerical solution of Fredholm integral-differential equations on unbounded domain
M. Matinfar A. Riahifar -
Open Access Article
108 - On edge detour index polynomials
Sh. Safari Sabet M. Farmani O. Khormali A. Mahmiani Z. Bagheri -
Open Access Article
109 - Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
H. R. Rezazadeh M. Maghasedi B. shojaee -
Open Access Article
110 - On the convergence of the homotopy analysis method to solve the system of partial differential equations
A. Fallahzadeh M. A. Fariborzi Araghi V. Fallahzadeh -
Open Access Article
111 - Operational matrices with respect to Hermite polynomials and their applications in solving linear differential equations with variable coefficients
Z. Kalateh Bojdi S. Ahmadi-Asl A. Aminataei -
Open Access Article
112 - Stochastic averaging for SDEs with Hopf Drift and polynomial diffusion coefficients
M. Alvand -
Open Access Article
113 - Second order linear differential equations with generalized trapezoidal intuitionistic Fuzzy boundary value
S. P. Mondal T. K. Roy -
Open Access Article
114 - Solution of the first order fuzzy differential equations with generalized differentiability
L. Jamshidi T. Allahviranloo -
Open Access Article
115 - Numerical solution of second-order stochastic differential equations with Gaussian random parameters
R. Farnoosh H. Rezazadeh A. Sobhani D. Ebrahimibagha -
Open Access Article
116 - Approximate solution of fourth order differential equation in Neumann problem
J. Rashidinia D. Kalvand L. Tepoyan -
Open Access Article
117 - Numerical Solution of Nonlinear System of Ordinary Differential Equations by the Newton-Taylor Polynomial and Extrapolation with Application from a Corona Virus Model
Bahman Babayar-Razlighi -
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118 - The combined reproducing kernel method and Taylor series for solving nonlinear Volterra-Fredholm integro-differential equations
Azizallah Alvandi Mahmoud Paripour -
Open Access Article
119 - Reproducing Kernel Space Hilbert Method for Solving Generalized Burgers Equation
M. Karimian A. Karimian -
Open Access Article
120 - Jacobi Operational Matrix Approach for Solving Systems of Linear and Nonlinear Integro-Differential Equations
Khadijeh Sadri Zainab Ayati -
Open Access Article
121 - On a modi cation of the Chebyshev collocation method for solving fractional diffiusion equation
Hosein jalebbonab Hojatollah Adibi -
Open Access Article
122 - Approximate solution of system of nonlinear Volterra integro-differential equations by using Bernstein collocation method
Sara Davaeifar Jalil Rashidinia -
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123 - The Tau-Collocation Method for Solving Nonlinear Integro-Differential Equations and Application of a Population Model
Atefeh Armand Zienab Gouyandeh -
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124 - Analytical Solution of Steady State Substrate Concentration of an Immobilized Enzyme Kinetics by Laplace Transform Homotopy Perturbation Method
Devipriya Ganeshan -
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125 - Numerical Solution of The Parabolic Equations by Variational Iteration Method and Radial Basis Functions
Sara Hosseini -
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126 - Solving a Class of Partial Differential Equations by Differential Transforms Method
Maryam Fahimi -
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127 - A Note on Solving Prandtl's Integro-Differential Equation
Atta Dezhbord Taher Lotfi -
Open Access Article
128 - A Novel Finite Difference Method of Order Three for the Third Order Boundary Value Problem in ODEs
Pramod Pandey -
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129 - Optimal Control of Hand, Foot and Mouth Disease Model using Variational Iteration Method
Devipriya Ganeshan L. Jane Darne -
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130 - Initial Value Problems for Fourth-Order Fuzzy Differential Equations by Fuzzy Laplace Transform
Hülya Gültekin Çitil -
Open Access Article
131 - Analytical Solution of the Effect of Awareness Program by Media on the Spread of an Infectious Disease by Homotopy Perturbation Method
Devipriya Ganeshan -
Open Access Article
132 - An explicit method for numerical solution of the equation governing the motion of a particle under arbitrary force fields
Ghiyam Eslami Masoumeh Zeinali -
Open Access Article
133 - NUMERICAL SOLUTION OF INTEGRO-DIFFERENTIAL EQUATION BY USING CHEBYSHEV WAVELET OPERATIONAL MATRIX OF INTEGRATION
M. A. Fariborzi Araghi S. Daliri M. Bahmanpour -
Open Access Article
134 - THE COMPARISON OF EFFICIENT RADIAL BASIS FUNCTIONS COLLOCATION METHODS FOR NUMERICAL SOLUTION OF THE PARABOLIC PDE’S
S. S. Mirshojaei S. Fayazzadeh -
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135 - HYBRID OF RATIONALIZED HAAR FUNCTIONS METHOD FOR SOLVING DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER
Y. Ordokhani N. Rahimi -
Open Access Article
136 - HAAR WAVELET AND ADOMAIN DECOMPOSITION METHOD FOR THIRD ORDER PARTIAL DIFFERENTIAL EQUATIONS ARISING IN IMPULSIVE MOTION OF A AT PLATE
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145 - Convergence of Legendre and Chebyshev multiwavelets in Petrov-Galerkin method for solving Fredholm integro-differential equations of high orders
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146 - Convergence of collocation Bernoulli wavelet method in solving nonlinear Fredholm integro-differential equations of fractional order
Abdolali Rooholahi Saeed AkhavanWe provide a computer method for solving fractional order nonlinear Fredholm integro-differential equations in this study. This method transforms the core issue into a set of algebraic equations using Bernoulli wavelets. The operational Bernoulli wavelet with fractional MoreWe provide a computer method for solving fractional order nonlinear Fredholm integro-differential equations in this study. This method transforms the core issue into a set of algebraic equations using Bernoulli wavelets. The operational Bernoulli wavelet with fractional integration is obtained and used. It works particularly well for technical applications. The convergence of the suggested strategy is the most crucial aspect to note here. The collocation approach for this issue has a unique approximation since these requirements can be shown using mathematical principles and matrices theory. Finally, some pertinent examples for which the exact solution is known are used in numerical simulation to confirm the effectiveness and relevance. Alternatively, these examples will demonstrate the viability and correctness of the suggested approach. We provide a computer method for solving fractional order nonlinear Fredholm integro-differential equations in this study. This method transforms the core issue into a set of algebraic equations using Bernoulli wavelets. The operational Bernoulli wavelet with fractional integration is obtained and used. It works particularly well for technical applications. The convergence of the suggested strategy is the most crucial aspect to note here. The collocation approach for this issue has a unique approximation since these requirements can be shown using mathematical principles and matrices theory. Finally, some pertinent examples for which the exact solution is known are used in numerical simulation to confirm the effectiveness and relevance. Alternatively, these examples will demonstrate the viability and correctness of the suggested approach. Manuscript profile -
Open Access Article
147 - حل عددی ارتعاشات پوسته استوانهای چند لایه با لایه پیزوالکتریک
عبدالمجید کنی اکبر علی بیگلودر این مقاله رفتار ارتعاشی پوسته­های چندلایه که سطوح داخلی و خارجی آنها مجهز به لایه­های حسگر و عملگر پیزوالکتریک می­باشد بررسی شده است. ابتدا پوسته چندلایه با تکیه­گاه­های ساده به روش تحلیلی بررسی و نتایج حاصل، با نتایج به دست آمده توسط سایر محققین Moreدر این مقاله رفتار ارتعاشی پوسته­های چندلایه که سطوح داخلی و خارجی آنها مجهز به لایه­های حسگر و عملگر پیزوالکتریک می­باشد بررسی شده است. ابتدا پوسته چندلایه با تکیه­گاه­های ساده به روش تحلیلی بررسی و نتایج حاصل، با نتایج به دست آمده توسط سایر محققین مقایسه شده است. آنگاه حل عددی به روش (GDQ) برای پوسته با لایه­های پیزوالکتریک و تکیه­گاه­های ساده، با حل تحلیلی آن مقایسه شده و در ادامه انواع شرایط تکیه­گاهی مورد مطالعه قرار گرفته است. با استفاده از معادلات حرکت، معادلات بنیادین و روابط کرنش- جابجایی، معادلات حالت- فضا حاصل می­شود که این معادلات با استفاده از تقریب لایه مجزا، به معادلات حالت- فضا با ضرایب ثابت تبدیل خواهند شد. سپس با استفاده از حل این معادلات می­توان فرکانس­های طبیعی پوسته در حالت تکیه­گاه ساده را به دست آورد. در صورتی که تکیه­گاه­ها غیر ساده باشند، حل معادلات دیفراسیل حالت- فضا به روش تحلیلی امکان­پذیر نبوده و باید از روش­های عددی کمک گرفت. روش یک چهارم تفاضلی روش عددی متداولی است که با تعداد کم نقاط نمونه، می­توان به جواب دقیق دست یافت. با استفاده از روش dq ، معادلات دیفرانسیل حالت- فضا حل شده و در نهایت با اعمال شرایط عاری از تراکشن سطوح بالا و پایین، می­توان به فرکانس­های طبیعی دست یافت. در نهایت تأثیر مستقیم و معکوس پیزوالکتریک، نسبت ضخامت لایه کامپوزیت به لایه پیزوالکتریک و نسبت شعاع میانی به ضخامت در رفتار ارتعاشی پوسته مورد بررسی قرار گرفته است Manuscript profile -
Open Access Article
148 - Direct method for solving nonlinear two-dimensional Volterra-Fredholm integro-differential equations by block-pulse functions
Elnaz Poorfattah Akbar Jafari Shaerlar
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