A novel fast modification of the Adomian decomposition method to solve integral equations of the first kind with hypersingular kernels

Abstract

In this paper, using the modified Adomian decomposition method, a novel fast scheme, has been presented, being interactive, to be used for solving a class of hypersingular integral equations of the first kind. Compared to the standard Adomian decomposition method, this method expedites the quick accumulation of a series of solutions. Different problems, for exemplification, have been solved in order to display the accuracy and validity of the aforementioned method. According to the results, it gets known that the novel fast modified Adomian decomposition method is so efficient and simple which gives the exact solution, and also shuns the complicated function of long theoretical calculations of collocation methods based on polynomial producing the exact solution.