On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis Method

被引：2
|
作者：
Rahby, A. S. [1 ]
Abdou, M. A. [2 ]
Mosa, G. A. [1 ]
机构：
[1] Benha Univ, Dept Math, Fac Sci, Banha 13518, Egypt
[2] Alexandria Univ, Fac Educ, Dept Math, Alexandria 21544, Egypt
来源：
INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS | 2022年 / 20卷
关键词：
nonlinear Fredholm-Volterra integral equations; Picard's method; homotopy analysis method and error analysis; NUMERICAL-SOLUTIONS; COLLOCATION METHOD;
D O I：
10.28924/2291-8639-20-2022-35
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we discuss the existence and uniqueness of the solution of the second kind nonlinear Volterra-Fredholm integral equations (NV-FIEs) which appear in mathematical modeling of many phenomena, using Picard's method. In addition, we use Banach fixed point theorem to show the solvability of the first kind NV-FIEs. Moreover, we utilize the homotopy analysis method (HAM) to approximate the solution and the convergence of the method is investigated. Finally, some examples are presented and the numerical results are discussed to show the validity of the theoretical results.
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页数：14
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