Numerical Solution of Systems of Integral Differential Equations by Using Modified Laplace-Adomian Decomposition Method

Abstract: In this work, we will employ the modified Laplace-Adomian decomposition method to present a general procedure for solving systems of integral differential equations. This method is modified of the combined form of the Laplace transform and Adomian Decomposition Method (MLADM). Illustrative examples are included to demonstrate the high accuracy and fast convergence of our method. Key words: Systems of integral differential equations • Laplace-Adomian decomposition method • Laplace transform • Adomian polynomials INTRODUTION Some important problems in science and engineering can usually be reduced to a system of integral and integral differential equations. Since few of these equations can be solved explicitly, it is often necessary to develop the numerical techniques which are appropriate combinations of numerical integration and interpolation [1, 2]. The aim of this study is to get solution of system of integral-differential equations as [3]: ( n)