Version 1
: Received: 8 May 2023 / Approved: 9 May 2023 / Online: 9 May 2023 (08:21:21 CEST)
How to cite:
Abusalim, S. M.; Abdou, M. A.; Abdel-Aty, M. A.; Nasr, M. E. Hybrid Functions Approach to Solving Nonlinear Integral Equations in Two Dimensions. Preprints2023, 2023050599. https://doi.org/10.20944/preprints202305.0599.v1
Abusalim, S. M.; Abdou, M. A.; Abdel-Aty, M. A.; Nasr, M. E. Hybrid Functions Approach to Solving Nonlinear Integral Equations in Two Dimensions. Preprints 2023, 2023050599. https://doi.org/10.20944/preprints202305.0599.v1
Abusalim, S. M.; Abdou, M. A.; Abdel-Aty, M. A.; Nasr, M. E. Hybrid Functions Approach to Solving Nonlinear Integral Equations in Two Dimensions. Preprints2023, 2023050599. https://doi.org/10.20944/preprints202305.0599.v1
APA Style
Abusalim, S. M., Abdou, M. A., Abdel-Aty, M. A., & Nasr, M. E. (2023). Hybrid Functions Approach to Solving Nonlinear Integral Equations in Two Dimensions. Preprints. https://doi.org/10.20944/preprints202305.0599.v1
Chicago/Turabian Style
Abusalim, S. M., Mohamed A. Abdel-Aty and Mohamed E. Nasr. 2023 "Hybrid Functions Approach to Solving Nonlinear Integral Equations in Two Dimensions" Preprints. https://doi.org/10.20944/preprints202305.0599.v1
Abstract
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
Keywords
Two- dimensional nonlinear integral equation; Banach fixed point theorem; Block-pulse function; Hybrid functions; Legendre polynomials
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.