The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions

This paper presents the application of Homotopy Analysis Method (HAM) for solving nonlinear system Volterra integral equations used to obtain a reasonably approximate solution. The HAM contains auxiliary parameter h which provides simple way adjust and control convergence region solution series. results show that is very effective method as well. were compared with solutions obtained by developing homotopy analysis using genetic algorithm (HAM-GA), considering residual error function fitness algorithm.