Solving Integro-Differential Equations by a Semi-Analytic Method

In this paper, we propose a method to obtain approximate solutions to Fredholm integral-differential equations by employing the homotopy analysis method (HAM). The HAM gives the possibility to increase convergence region and rate of series solution. we show that the adomian decomposition method (ADM) cannot give better results than the present method. Five examples are presented to illustrate convergence and accuracy of the method to the solution. Also, we compute the absolute error to show that obtained results have reasonable accuracy.