具有奇异核的相位滞后volterra-fredholm积分方程的解析与数值讨论

IF 1 4区数学 Q3 MATHEMATICS, APPLIED Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI:10.11948/20220547

Mohammed Abdel-Aty, Mohammed Abdou

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引用次数: 0

摘要

本文研究了第二类Volterra-Fredholm积分方程(V-FIESK)的存在性和唯一解。一般奇异核被认为在Fredholm积分项的位置上。奇异核在特殊条件和新的讨论下趋向于对数函数。采用Legendre多项式求解对数形式的Volterra- fredholm积分方程，其中Volterra积分项的核是时间上的一个正连续函数。通过对该问题的级数求解，得到了一个无穷线性代数方程组，并讨论了该方程组的收敛性。最后，在得到数值结果后，利用Maple软件计算误差。

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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ANALYTICAL AND NUMERICAL DISCUSSION FOR THE PHASE-LAG VOLTERRA-FREDHOLM INTEGRAL EQUATION WITH SINGULAR KERNEL

In this paper, we studied the existence and unique solution of the Volterra-Fredholm integral equation of the second kind (V-FIESK). The general singular kernel is considered to be in position with the Fredholm integral term. Singular kernel will tend to a logarithmic function under exceptional conditions and new discussions. The Volterra-Fredholm integral equation with the logarithmic form will be solved using Legendre polynomials, where the kernel of Volterra integral term is a positive continuous function in time. A system of infinite linear algebraic equations is obtained by solving the problem in series, where the convergence of this system is discussed. Finally, The error is calculated using Maple software after the numerical results have been acquired.

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来源期刊

Journal of Applied Analysis and Computation MATHEMATICS, APPLIED-

CiteScore

2.30

自引率

9.10%

发文量

期刊介绍： The Journal of Applied Analysis and Computation (JAAC) is aimed to publish original research papers and survey articles on the theory, scientific computation and application of nonlinear analysis, differential equations and dynamical systems including interdisciplinary research topics on dynamics of mathematical models arising from major areas of science and engineering. The journal is published quarterly in February, April, June, August, October and December by Shanghai Normal University and Wilmington Scientific Publisher, and issued by Shanghai Normal University.