Analytical Approximations for Nonlinear Integro-Differential Equations

Abstract

In this work, we are concerned with how to find a solution for the nonlinear integral andointegro-differentialeequationsuusingttwoomethodsoLaplaceotransformiseries idecomposition method (LTSDM) and Sumuduutransform series decomposition method (STSDM). In these methods, the nonlinear part of the equation described in Adomian idecomposition series. The Laplace and Sumudu methods are found to be reliable and accurate. Four examples are discussed to check the applicability and the simplicity of these methods. Finally, the results are tabulated and displayed graphically to make comparisons between the approximate and exact solutions.

Keywords

• Nonlinear Intgro-Differential Equation of Second Kind, Adomian Decomposition Method, Laplace Transform, Sumudu Transform.