Usage of numerical methods to solve nonlinear mixed Volterra-Fredholm integral equations and their system

Abstract

In this paper, we apply the homotopy perturbation method (HPM), modified homotopy perturbation method(MHPM), variational iteration method (VIM), Adomian decomposition method (ADM), and modified Adomian decomposition method (MADM) to solve nonlinear mixed Volterra-Fredholm integral equations and itssystem. We investigate the approximate solution of this equation and its system via proposed methods. Thevalidity and efficiency of these methods are demonstrated through various numerical examples that illustratethe efficiency, accuracy, and simplicity of the proposed methods. Moreover, the convergence and uniquenessof the solution of the suggested methods are confirmed and compared with the exact solutions.