Two-Dimensional Fredholm Integro-Differential Equation with Singular Kernel and Its Numerical Solutions

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Advances in Mathematical Physics Pub Date : 2022-12-08 DOI:10.1155/2022/2501947

A. M. Al-Bugami

引用次数: 1

Abstract

In this paper, we introduce the nonlinear Fredholm integro-differential equation of the second kind with singular kernel in two-dimensional NT-DFIDE. Furthermore, we study this new equation numerically. The existence of a unique solution of the equation is proved. The numerical results of NT-DFIDE are obtained by the following methods: Toeplitz matrix method (TMM) and product Nystrom method (PNM). The given applications showed the efficiency of these methods.

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具有奇异核的二维Fredholm积分微分方程及其数值解

本文在二维NT-DFIDE中引入了一类二阶奇异核的非线性Fredholm积分微分方程。并对该方程进行了数值研究。证明了该方程唯一解的存在性。采用Toeplitz矩阵法(TMM)和product Nystrom法(PNM)对nt - dfid进行了数值计算。给出的应用表明了这些方法的有效性。

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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来源期刊

Advances in Mathematical Physics 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

151

审稿时长

>12 weeks

期刊介绍： Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.