Partial Differential Equation

Open Access Article

1 - Solving random inverse heat conduction problems using PSO and genetic algorithms
I. Hossein Zade Shahbolaghi R. Pourgholi H. Dana Mazraeh S.H. Tabasi

The 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 More

The 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

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2 - 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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3 - 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

Open Access Article

4 - A semi-analytic method to solve the oxygen diffusion problem
Mojtaba Moradipour

10.30495/JNRM.2022.56774.1991

In 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 More

In 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

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5 - An application of fuzzy fractional partial differential equations on heart sound signal denoising
farnoosh karimi Tofigh Allahviranloo Saeed Abbasbandy

Cardiovascular 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 More

Cardiovascular 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

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6 - 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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7 - Partial Differential Equations applied to Medical Image ‎Segmentation
B. Bagheri R. Ezzati

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8 - A Second-Order Accurate Numerical Approximation for Two-Sided Fractional Boundary Value Advection-Diffusion Problem
Elyas Shivanian Hamid Reza Khodabandehlo

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

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10 - 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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