Hybrid Functions Approach to Solving Nonlinear Integral Equations in Two Dimensions

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