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求解非线性Volterra-Fredholm积分微分方程的同伦分析方法的收敛性研究。

The convergence study of the homotopy analysis method for solving nonlinear Volterra-Fredholm integrodifferential equations.

作者信息

Ghanbari Behzad

机构信息

Department of Basic Sciences, Kermanshah University of Technology, P.O. Box 63766-67178, Kermanshah, Iran.

出版信息

ScientificWorldJournal. 2014 Jan 12;2014:465951. doi: 10.1155/2014/465951. eCollection 2014.

DOI:10.1155/2014/465951
PMID:24624043
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC3939014/
Abstract

We aim to study the convergence of the homotopy analysis method (HAM in short) for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.

摘要

我们旨在研究用于求解特殊非线性沃尔泰拉 - 弗雷德霍姆积分微分方程的同伦分析方法（简称为HAM）的收敛性。简要讨论了该方法收敛的充分条件。还给出了一些示例以证明该技术的有效性和适用性。将所得结果与精确解进行比较表明，该方法可靠且能够为求解此类方程提供解析处理。

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