Solving fuzzy differential equations by differential transformation method (original) (raw)

Two Successive Schemes for Numerical Solution of Linear Fuzzy Fredholm Integral Equations of the Second Kind

… Journal of Basic and Applied Sciences, 2010

In this paper, two successive schemes for solving linear fuzzy Fredholm integral equations are presented. Using the parametric form of fuzzy numbers, we convert linear fuzzy Fredholm integral equation of the second kind to a linear system of integral equations of the second kind in the crisp case. We use two schemes, successive approximation and Taylor-successive approximation methods, to find the approximate solutions of the converted system, which are the approximate solutions for the fuzzy Fredholm integral equation of the second kind. The proposed methods are illustrated by two numerical examples.

Usage of the Fuzzy Laplace Transform Method for Solving One-Dimensional Fuzzy Integral Equations

EQUATIONS, 2022

In this paper, we propose the solution of fuzzy Volterra and Fredholm integral equations with convolution type kernel using fuzzy Laplace transform method (FLTM) under Hukuhara differentiability. It is shown that FLTM is a simple and reliable approach for solving such equations analytically. Finally, the method is illustrated with few examples to show the ability of the proposed method.

Solving Fuzzy Integral Equations of the Second Kind by Fuzzy Laplace Transform Method

2012

Abstract Using fuzzy Laplace transform method, the solution of fuzzy convolution Volterra integral equation (FCVIE) of the second kind with convolution fuzzy and crisp kernel is investigated. So, fuzzy convolution operator is proposed and related theorem is submitted which is useful for solving FCVIEs. Finally, several illustrative examples with fuzzy and crisp convolution kernels are given to show the ability of the proposed method.

Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method

Applied Mathematics and Computation, 2005

Using parametric form of fuzzy numbers we convert a linear fuzzy Fredholm integral equation of the second kind to a linear system of integral equations of the second kind in crisp case. We use Adomian method and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equation of the second kind. We apply the method to some examples. Ó 2004 Elsevier Inc. All rights reserved.

Solving fuzzy Volterra integro-differential equation by fuzzy differential transform method

In this study, differential transform method (DTM) is applied to fuzzy integro-differential equation. The concept of generalized Hdifferentiability is used. If the equation has a solution in terms of the series expansion of known functions; this powerful method catches the exact solution. Some numerical examples are also given to illustrate the superiority of the method. All rights reserved.

A Numerical Study for Solving the Systems of Fuzzy Fredholm Integral Equations of the Second Kind Using the Adomian Decomposition Method

Iraqi journal of science, 2023

In this paper, the Adomian decomposition method (ADM) is successfully applied to find the approximate solutions for the system of fuzzy Fredholm integral equations (SFFIEs) and we also study the convergence of the technique. A consistent way to reduce the size of the computation is given to reach the exact solution. One of the best methods adopted to determine the behavior of the approximate solutions. Finally, the problems that have been addressed confirm the validity of the method applied in this research using a comparison by combining numerical methods such as the Trapezoidal rule and Simpson rule with ADM.

Applications of the double fuzzy Sumudu transform for solving Volterra fuzzy integral equations

In this paper, we use double fuzzy Sumudu transform method (DSTM) to solve two dimensional fuzzy convolution Volterra integral equations (2D-FCVIE). By using double fuzzy Sumudu transform method the problem reducing to algebraic problem.The convolution, its properties and convolution theorem with a proof are discussed in some detail. We give some preliminary results of the double fuzzy Sumudu transform method and describe the method of this paper. Finally, illustrative example with fuzzy and crisp convolution kernels is given to show the ability of the proposed method.