‎ Differential equations

Open Access Article

1 - Analytical approach for the use of different gauges in bubble wakefield acceleration
Hitendra Malik Sonu Kumar Vidushi Dhaka Dhananjay Singh

10.30495/jtap.152102

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2 - Computational Method for Fractional-Order Stochastic Delay Differential Equations
Behrouz Parsa Moghaddam Zeynab Salamat Mostaghim Elham Alsaddat Hashemi Zadeh

Dynamic 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 More

Dynamic 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

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3 - Zernike radial polynomials method for solving nonlinear singular boundary value problems arising in physiology
M.A. Ebadi E.S. Hashemizadeh A.H. Refahi Sheikhani

The 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 More

The 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

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4 - Numerical Solution and Error Analysis for Linear and Nonlinear Delay Differential Equations
Ebrahim Amini Ali Ebadian

In 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 More

In 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

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5 - The new implicit finite difference scheme for two-sided space-time fractional partial differential equation
Hamid Reza Khodabandehlo Elyas Shivanian Shaaban Mostafaee

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 solv More

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./////////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

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6 - Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes
A. Momeni M. Kamrani

Ordinary 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 More

Ordinary 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

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7 - Existence solutions for new p-Laplacian fractional boundary value problem with impulsive effects
N. Nyamoradi A. Razani

Fractional 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 More

Fractional 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

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8 - On the structural properties for the cross product of fuzzy numbers with applications
Robab Alikhani

In 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 More

In 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

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9 - Analytical solutions of differential equations based on genetic meta-heuristic algorithm and ant colony optimization
Nasser Mikaeilvand Akram Javadi Hassan Hosseinzadeh

Many 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 More

Many 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

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10 - Numerical solution of fractional model of HIV infection in cells CD4+T
Mohammad Reza Doostar Tayebeh Damercheli Alireza Vahidi

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 More

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. 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

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11 - Existence of fixed points for generalized α-admissible Geraghty and application to solution of nonlinear differential equations
Babak Mohammadi Vahid Parvaneh Farhan Golkarmanesh

Recently, 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 More

Recently, 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

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12 - Estimating the half-life of stock price mean reverting: an application of Stochastic Differential Equations
hadi rahmani fazli ahmad molabahrami

In 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 More

In 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

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13 - The generalized variational iteration method to solve the fractal partial differential equations
Homa Afraz Alireza Khalili Golmankhaneh

10.30495/jnrm.2022.69663.2328

Fractional 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 More

Fractional 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

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14 - Legendre pseudo-spectral method for solving multi-pantograph delay differential equations
Mohammad Hadi Noori Skandari Mostafa Mahmoudi Javad Vahidi Mehdi Ghovatmand

10.30495/jnrm.2022.59953.2072

Delay 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 More

Delay 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

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15 - Approximated solution of First order Fuzzy Differential Equations under generalized differentiability
T. Allahviranloo N. Ahmady E. Ahmady

In 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 More

In 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

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16 - Numerical Solution of fuzzy differential equations of nth-order by Adams-Bashforth method
N. Parandin

So 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 More

So 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

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17 - A Numerical Method for Solving Fuzzy Differential Equations With Fractional Order
N. Ahmady

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18 - حل مسائل مقدار اولیه کوشی – اویلر فازی مرتبه دوم تحت مشتق پذیری توسعه یافته
مهران چهلابی

10.30495/ijim.2022.19222

در 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 More

در 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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19 - A Fuzzy Power Series Method for Solving Fuzzy Differential Equations With Fractional Order
E. Ahmady

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20 - یک روش مستقیم برای حل معادلات دیفرانسیل تاخیری خطی
E. Zeynal E. Babolian T. Damercheli

در 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 More

در 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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21 - جواب عددی از معادلات دیفرانسیل فازی هیبریدی مرتبه دوم با دیفرانسیل پذیری تعمیم یافته
نیره شهریاری سعید عباسبندی

در 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& More

در 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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22 - یک روش عددی سریع براساس توابع ترکیبی تیلور و بلاک پالس برای حل معادلات دیفراسیل تاخیری
مهدی ابلاغی علیرضا وحیدی اسماعیل بابلیان

در 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 More

در 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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23 - 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 عباسبندی

10.30495/ijim.2022.64043.1555

در 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 More

در 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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24 - Solution of fuzzy differential equations
M. Otadi M. Mosleh

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25 - Approximate Solution of Fuzzy Fractional Differential Equations
A. Panahi

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26 - A Piecewise Approximate Method for Solving Second Order Fuzzy Differential Equations Under Generalized ‎Differentiability‎
E. Ahmady N. Ahmady

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27 - Generalized H-differentiability for solving second order linear fuzzy differential ‎equations
P. Darabi S. Moloudzadeh&lrm; H. Khandani&lrm;

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28 - Partial Differential Equations applied to Medical Image ‎Segmentation
B. Bagheri R. Ezzati

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29 - Modified homotopy perturbation method for solving non-linear oscillator's ‎equations
A. R. Vahidi Z. Azimzadeh M. Shahrestani&lrm;

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30 - An approximate method for solving fractional system differential equations
Mohammad Adabitabar Firozja Bahram Agheli

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31 - Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations
Khalid Aboodh

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32 - Confidence Interval for Solutions of the Black-Scholes Model
Mehran Paziresh Mohamad Ali Jafari Majid Feshari

10.22034/amfa.2019.1869742.1231

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33 - Numerical Simulation and Methodology Based on Improved Split Step Method for Studying Stochastic Models
Leila Torkzadeh Hassan Ranjbar

10.30495/fomj.2021.685942

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34 - اسـتفاده از تجزیـه و تحلیـل تقـارن لـی بـرای معـادلات دیفرانسـیل جزئـی مرتبـه دوم
موسی ایلی جعفر بی آزار زینب آیتی

بـه 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 More

بـه 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

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35 - بهینه سازی معادلات دیفرانسیل خنثی با استفاده از روش MHAM و RSK
شادان صدیق بهزادی

در 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 More

در 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

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36 - حل عددی معادلات دیفرانسیل کسری زمانی فوکر-پلانک -کولموگروف با استفاده از روش موجک هار و بررسی همگرایی و خطا
شعبان محمدی S. Reza Hejazi

هدف 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 More

هدف 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

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37 - تقارنهای لی ، خود الحاقی و قوانین بقا معادله مونج آمپر
زهرا مومن نژاد مهدی نجفی خواه

این 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 More

این 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

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38 - SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS UNDER GENERALIZED DIFFERENTIABILITY BY ADOMIAN DECOMPOSITION METHOD
ت. اللهویرانلو ل. جمشیدی

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39 - Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant
Anil Kr. Aggarwal Sanjeev Kumar Vikram Singh Tarun Kr. Garg

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40 - Investigating and Improving the Uncertainty of Control Systems Using Fuzzy Differential Equations
Fateme Arab

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41 - Modeling of Gold coin futures with stochastic differential equations
Rahele Baqeri mohammadreza setayesh Reza Radfar

The 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 More

The 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

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42 - Comparison of the performance of Merton and Heston models in predicting the price of gold coin futures contracts
Rahele Baqeri mohammadreza setayesh

Today, 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 More

Today, 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

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43 - Initial value problems for second order hybrid fuzzy differential equations
M. Otadi

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44 - Application of DJ method to Ito stochastic differential equations
H. Deilami Azodi

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45 - On the convergence of the homotopy analysis method to solve the system of partial differential equations
A. Fallahzadeh M. A. Fariborzi Araghi V. Fallahzadeh

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46 - 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

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47 - Solution of the first order fuzzy differential equations with generalized differentiability
L. Jamshidi T. Allahviranloo

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48 - 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

10.30495/ijm2c.2021.685126

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49 - Numerical Solution of The Parabolic Equations by Variational Iteration Method and Radial Basis Functions
Sara Hosseini

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50 - Optimal Control of Hand, Foot and Mouth Disease Model using Variational Iteration Method
Devipriya Ganeshan L. Jane Darne

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51 - 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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52 - APPLICATION OF DIFFERENTIAL TRANSFORM METHOD TO SOLVE HYBRID FUZZY DIFFERENTIAL EQUATIONS
Mahmoud Paripour Homa Heidari Elahe Hajilou

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53 - APPLICATION NEURAL NETWORK TO SOLVE ORDINARY DIFFERENTIAL EQUATIONS
Nouredin Parandin Somayeh Ezadi

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54 - حل عددی ارتعاشات پوسته استوانه‌ای چند لایه با لایه پیزوالکتریک
عبدالمجید کنی اکبر علی بیگلو

در 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 More

در 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

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