Solving Nonlinear Integro-Differential Equations Using the Combined Homotopy Analysis Transform Method With Adomian Polynomials

In this paper, we propose a reliable combination of the homotopy analysis method (HAM) and laplace transform-Adomian method to find the analytic approximate solution for nonlinear integro-differential equations. In this technique, the nonlinear term is replaced by its Adomian polynomials for the index k, and hence the dependent variable components are replaced in the recurrence relation by their corresponding homotopy analysis transforms components of the same index. Thus, the nonlinear integro-differential equation can be easily solved with less computational work for any analytic nonlinearity due to the properties and available algorithms of the Adomian polynomials. The results show that the method is very simple and effective.