Laplace transform and adomian decomposition methods for solving nonlinear volterra integro-differential equations

Abstract

Since its introduction in the 1980s, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method when used for solve nonlinear Volterra integro-differential equations and also the combined form of the Laplace transform method with the Adomian decomposition method is effectively and useful way to develop an analytic treatment for many types of equations, linear and nonlinear ordinary differential equations (ODE), linear and nonlinear partial differential equations (PDE). In this study will combined Laplace transform-Adomian decomposition method to solve nonlinear Volterra integro-differential equations, this study is divided into five Chapters. The first chapter is devoted to an introduction, the second is devoted to the literature review, and Chapter 3 devoted to research methodology, Chapter 4 presents the solution for the nonlinear Volterra integro-differential equation. Finally, the Chapter 5 is devoted to the conclusion and recommendations based on this study.