Analytical and Numerical Discussion for the Quadratic Integral Equations

Abstract

In this work, we study the existence and uniqueness 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 (HPM) is presented to obtain an approximate solution of quadratic integral equation with phase--lag term. Convergence and error estimate of HPM are obtained. HPM is a powerful device for solving a wide variety of problems. 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.