Adomian Decomposition Method - Chakraverty, Snehashish; Mahato, Nisha; Karunakar, Perumandla; Dilleswar Rao, Tharasi (Advanced Numerical and Semi-Analytical Methods for Differential Equations, 2019)
The Adomian decomposition method (ADM) is an efficient semi‐analytical technique used for solving linear and nonlinear differential equations. It permits us to handle both nonlinear initial value problems (IVPs) and boundary value problems. The solution technique of this method is mainly based on decomposing the solution of nonlinear operator equation to a series of functions. Each presented term of the obtained series is developed from a polynomial generated in the expansion of an analytic function into a power series. This chapter presents procedures for solving linear as well as nonlinear ordinary/partial differential equations by the ADM along with example problems for clear understanding. It also presents linear and nonlinear IVPs for clear understanding of the ADM for ordinary differential equations. ADM transforms system of partial differential equations into a set of recursive relation that can easily be handled. To understand the method, one can consider the system of linear partial differential equations.