Application of Homotopy Analysis Method for Solving Systems of Volterra Integral Equations (Advances in Applied Mathematics and Mechanics, 2012)
In this paper, we prove the convergence of homotopy analysis method (HAM).We also apply the homotopy analysis method to obtain approximateanalytical solutions of systems of the second kind Volterra integral equations. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence regionof series solutions. It is shown that the solutions obtained by  thehomotopy-perturbation method (HPM) are only special cases of the HAMsolutions. Several examples are given to illustratethe efficiency and implementation of the method.