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

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