Hybrid Functions Approach to Solving Nonlinear Integral Equations in Two Dimensions

Sahar M. Abusalim; Mohamed A. Abdou; Mohamed A. Abdel-Aty; Mohamed E. Nasr

doi:10.20944/preprints202305.0599.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 8 May 2023 / Approved: 9 May 2023 / Online: 9 May 2023 (08:21:21 CEST)

This study presents the solution of the second type of a two-dimensional nonlinear integral equation in Banach space. Also, the existence and uniqueness of this equation’s solution are discussed. We utilize a numerical approach involving hybrid and block-pulse functions to obtain the approximate solution of a two-dimensional nonlinear integral equation. Nonlinear integral equation in two dimensions is reduced numerically to a system of nonlinear algebraic equations that can be solved using numerical methods. This study focuses on showing the convergence analysis for the numerical approach and obtaining an error estimate. Some numerical examples have been provided to demonstrate the approach’s viability and efficacy

Two- dimensional nonlinear integral equation; Banach fixed point theorem; Block-pulse function; Hybrid functions; Legendre polynomials

Computer Science and Mathematics, Mathematics

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Hybrid Functions Approach to Solving Nonlinear Integral Equations in Two Dimensions

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