New algorithms for solving nonlinear mixed integral equations-Reference-Cited by-同舟云学术

New algorithms for solving nonlinear mixed integral equations

Published:2023 Issue:11 Volume:8 Page:27488-27512
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Matoog R. T.¹,Abdou M. A.²,Abdel-Aty M. A.³

Affiliation:

1. Department of Mathematics, Faculty of Applied Sciences, Umm Al–Qura University, Makkah, Saudi Arabia

2. Department of Mathematics, Faculty of Education, Alexandria University, Alexandria 21511, Egypt

3. Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt

Abstract

<abstract><p>In this article, the existence and unique solution of the nonlinear Volterra-Fredholm integral equation (NVFIE) of the second kind is discussed. We also prove the solvability of the second kind of the NVFIE using the Banach fixed point theorem. Using quadrature method, the NVFIE leads to a system of nonlinear Fredholm integral equations (NFIEs). The existence and unique numerical solution of this system is discussed. Then, the modified Taylor's method was applied to transform the system of NFIEs into nonlinear algebraic systems (NAS). The existence and uniqueness of the nonlinear algebraic system's solution are discussed using Banach's fixed point theorem. Also, the stability of the modified error is presented. Some numerical examples are performed to show the efficiency and simplicity of the presented method, and all results are obtained using Wolfram Mathematica 11.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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