Numerical Solution of Nonlinear Quadratic Integral Equation of Hammerstein Type Based on Fixed-Point Scheme

Reza Mollapourasl () and Joseph Siebor
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Reza Mollapourasl: Department of Mathematics, Farmingdale State College—SUNY, Farmingdale, NY 11735, USA
Joseph Siebor: Department of Mathematics, Farmingdale State College—SUNY, Farmingdale, NY 11735, USA

Mathematics, 2025, vol. 13, issue 9, 1-15

Abstract: Existence of the solution for the nonlinear quadratic integral equation of the Hammerstein type in the Banach space BC( R + ) has been proved by using the technique of measure of noncompactness and fixed-point theorem. In this article, we obtain an approximate solution for the quadratic integral equation by using the Sinc method and the fixed-point technique. Moreover, the convergence of the numerical scheme for the solution of the integral equation is demonstrated by a theorem, and numerical experiments are presented to show the accuracy of the numerical scheme and guarantee the analytical results.

Keywords: Sinc method; measure of noncompactness; fixed-point method; convergence; nonlinear hammerestein integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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