Analytical and numerical discussion for the quadratic integral equations

M A Abdel ; Aty ; M A Abdou

Filomat, Tome 37 (2023) no. 24, p. 8095

Résumé

In this work, we study the existence of at least one solution of the Quadratic integral equation with Phase–lag term. Our proof depends on a suitable combination of the Darbo's fixed point principle and the technique of measures of noncompactness. Homotopy perturbation method is presented to obtain an approximate solution of Quadratic integral equation with Phase–lag term. Convergence and error estimate of Homotopy perturbation method are obtained. Homotopy perturbation method is a powerful device for solving a wide variety of problems. It gives excellent flexibility to the expression of the solution and how the solution is explicitly obtained, and provides great freedom in choosing the base functions of the desired solution and the corresponding auxiliary linear operator of homotopy. These methods produce the solutions in terms of convergent series without needing to restrictive assumptions, to illustrate the ability and credibility of the methods, we deal with two examples that show simplicity and effectiveness.

Détail

DOI : 10.2298/FIL2324095A

Classification : 45A05, 47G10, 47H09, 47H10, 65R20
Keywords: Quadratic integral equation, Phase–Lag, Measure of noncompactness, Darbo’s fixed point theorem, Nondecreasing solutions, Homotopy perturbation method