求解模糊Volterra-Fredholm积分方程的改进Adomian分解方法

Q4 Mathematics

Journal of the Indian Mathematical Society Pub Date : 2018-01-04 DOI:10.18311/JIMS/2018/16260

Ahmed A. Hamoud, K. Ghadle

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引用次数: 55

摘要

本文应用一种改进的Adomian分解方法来逼近第一类和第二类模糊Volterra—Fredholm积分方程的解。在此基础上，将一个模糊的Volterra—Fredholm积分方程在清晰的情况下转化为一个Volterra—Fredholm积分方程组。我们使用MADM来寻找该系统的近似解，从而获得模糊Volterra-Fredholm积分方程的模糊解的近似值。研究了一个非线性演化模型。此外，我们还将证明该方法解的存在性、唯一性和收敛性。并通过算例验证了该方法的有效性和适用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Modified Adomian Decomposition Method for Solving Fuzzy Volterra-Fredholm Integral Equation

In this paper, a modied Adomian decomposition method has been applied to approximate the solution of the fuzzy Volterra-Fredholm integral equations of the first and second Kind. That, a fuzzy Volterra-Fredholm integral equation has been converted to a system of Volterra-Fredholm integral equations in crisp case. We use MADM to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the Fuzzy Volterra-Fredholm integral equation. A nonlinear evolution model is investigated. Moreover, we will prove the existence, uniqueness of the solution and convergence of the proposed method. Also, some numerical examples are included to demonstrate the validity and applicability of the proposed technique.

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来源期刊

Journal of the Indian Mathematical Society Mathematics-Mathematics (all)

CiteScore

0.50

自引率

0.00%

发文量

期刊介绍： The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.