Adomian Decomposition Method

Abstract

The Adomian decomposition method (ADM) is an important semi-analytical technique used to solve linear and nonlinear differential equations. It helps us to manage both the nonlinear initial value problems (IVPs) and boundary value problems (BVPs). This technique is based primarily on decomposing nonlinear operator equations into a series of functions. Each term of the obtained series is constructed from a polynomial generated by expanding an analytic function into a power series. This chapter discusses the procedure for solving linear and nonlinear fractional partial differential equations (PDEs) by using the ADM along with examples for clear understanding. ADM converts the structure of PDEs into an easily accessible series of recursive relationships. The test problems used in this chapter demonstrate that ADM is an efficient method for solving linear/nonlinear fractional differential equations. Generally, the series converges with an increase in terms, but it is not always possible to have a compact solution.