An analytical method for solving singular integral equations of Abel type

摘要

Approximate analytical solution to a class of Abel type integral equations is obtained here by using the homotopy analysis method. This method appears to be quite powerful and efficient compared to the homotopy perturbation method (HPM) and the Adomian decomposition method (ADM). The validity and applicability of the present method is illustrated through a number of examples thus demonstrating its efficiency and also simplicity in solving these types of integral equations compared to the other existing methods like HPM and ADM.