Analytical Solution of Integro-Differential Equations by Using Modified Laplace Transform a Domian Decomposition Method.

Abstract

Nowadays integrodifferential equations are used in various fields of sciences and engineering. Recently most of researchers have taken considerable effort to the study of exact and numerical solutions of the linear, nonlinear ordinary, or partial differential equations. In this paper, we have discussed the modified Laplace transform Adomian decomposition method (MLTADM) which is the combination of Laplace transform and Adomian decomposition method to solve the second and third-order nonlinear integrodifferential equations. The main advantage of this method is the fact that it gives an analytical solution. The method overcomes the difficulties arising in calculating the Adomian polynomials. The efficiency of the method was tested on some numerical examples, and the results show that the method is easier than many other numerical techniques. It is also observed that (MLTADM) is a reliable tool for the solution of linear and nonlinear integrodifferential equations.