On the numerical solution of Fredholm-type integro-differential equations using an efficient modified Adomian decomposition method

The efficiency of the Adomian decomposition method in the solution of integro-differential equations cannot be overemphasized. However, improvement of the method is needed as its drawbacks have been analyzed and reported in recent literature. This present work develops a new modification of the method and its implementation on linear Fredholm type of integro-differential equations. The approach is based on the modification of the traditional Adomian decomposition method. The idea employs the Taylor series expansion of the source term whose resulting functions were combined in two terms for predicting the solution in each iteration. This approach yields a very high accuracy degree when compared to related methods in literature. The newly proposed method is said to accelerate and converges faster than the standard Adomian Decomposition Method. The procedure proves to be concise, effective and converges faster to the true solution of linear Fredholm Integro-differential problems.