A novel computing multi-parametric homotopy approach for system of linear and nonlinear Fredholm integral equations

Abstract

This paper suggests a novel multi-parametric homotopy method for systems of Fredholm integral equations. This modified method contains three convergence-control parameters to form an improved homotopy. We present efficient error estimation for the approximate solution. The results of present method are compared with the Adomian decomposition method (ADM), the homotopy perturbation method (HPM) and standard homotopy analysis method results that provides confirmation for the validity of proposed approach. Some test examples are given to clarify the efficiency and high accuracy of the present method. The results reveal that the present method is very effective and convenient.