The behaviour of the maximum and minimum error for Fredholm-Volterra integral equations in two-dimensional space

被引：8

作者：

Abdou, M. A. ^{[1
]}

Elhamaky, M. N. ^{[2
]}

Soliman, A. A. ^{[2
]}

Mosa, G. A. ^{[2
]}

机构：

[1] Alexandria Univ, Fac Educ, Dept Math, Alexandria 21526, Egypt

[2] Benha Univ, Fac Sci, Dept Math, Banha 13518, Egypt

来源：

JOURNAL OF INTERDISCIPLINARY MATHEMATICS | 2021年 / 24卷 / 08期

关键词：

Fredholm-Volterra integral equation; Banach's fixed point theorem; Collocation method; Galerkin method; Maximum error; Minimum error; NUMERICAL-METHOD; 2ND KIND; COLLOCATION;

D O I：

10.1080/09720502.2020.1814497

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the behaviour of the maximum (Max.) and minimum (Min.) error for Fredholm-Volterra integral equations (F-VIEs) of the second kind using Collocation (CM) and Galerkin (GM) methods by choosing N-linearly independent functions. The approximate solution is obtained by two techniques; the first technique (1st TM) depends on representing F-VIE as a system of Fredholm integral equations (FIEs) of the second kind where the approximate (Appr.) solution is obtained as functions of x at fixed times. In the second technique (2nd TM), we represent the approximate solution as a sum of functions of x and t. Furthermore, the comparisons between the results which are obtained by two techniques in each method are devoted and the results are represented in group of figures and tables.

引用

页码：2049 / 2070

页数：22

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