Abstract
In this paper, we propose a new numerical method for solving system of integro-differential equations featuring Volterra and Fredholm integrals. The proposed method depends on the successful application of the Discrete Adomian Decomposition Method (DADM) to solve highly complicated functional equations coupled with some numerical integration schemes of Trapezoidal and Simpson rules. The scheme is further simulated with the aid of symbolic computation and demonstrated on some test problems. We then carried out error analysis in comparison with some existing methods revealed that the present method is superior due to the high level of accuracy and less computational steps.