New algorithms for solving nonlinear mixed integral equations

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...

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Published in:AIMS mathematics Vol. 8; no. 11; pp. 27488 - 27512
Main Authors: Matoog, R. T., Abdou, M. A., Abdel-Aty, M. A.
Format: Journal Article
Language:English
Published: AIMS Press 01.01.2023
Subjects:
banach fixed point theorem
modified taylor's method
nonlinear algebraic system
nonlinear volterra-fredholm integral equation
picard's method
system of nonlinear fredholm integral equations
ISSN:2473-6988, 2473-6988
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Abstract 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.
AbstractList 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.
Author Abdel-Aty, M. A.
Matoog, R. T.
Abdou, M. A.
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Snippet 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...
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SubjectTerms banach fixed point theorem
modified taylor's method
nonlinear algebraic system
nonlinear volterra-fredholm integral equation
picard's method
system of nonlinear fredholm integral equations
Title New algorithms for solving nonlinear mixed integral equations
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