Hybrid Functions Approach via Nonlinear Integral Equations with Symmetric and Nonsymmetrical Kernel in Two Dimensions

Autor:	Sahar M. Abusalim, Mohamed A. Abdou, Mohamed A. Abdel-Aty, Mohamed E. Nasr
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	nonlinear integral equation symmetric and nonsymmetrical kernel Banach fixed point theorem block-pulse function hybrid functions Legendre polynomials Mathematics QA1-939
Zdroj:	Symmetry, Vol 15, Iss 7, p 1408 (2023)
Druh dokumentu:	article
ISSN:	2073-8994 42529905
DOI:	10.3390/sym15071408
Popis:	The second kind of two-dimensional nonlinear integral equation (NIE) with symmetric and nonsymmetrical kernel is solved in the Banach space L2[0,1]×L2[0,1]. Here, the NIE’s existence and singular solution are described in this passage. Additionally, we use a numerical strategy that uses hybrid and block-pulse functions to obtain the approximate solution of the NIE in a two-dimensional problem. For this aim, the two-dimensional NIE will be reduced to a system of nonlinear algebraic equations (SNAEs). Then, the SNAEs can be solved numerically. This study focuses on showing the convergence analysis for the numerical approach and generating an estimate of the error. Examples are presented to prove the efficiency of the approach.
Databáze:	Directory of Open Access Journals
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