The Adomian decomposition method for solving a system of non-linear equations.

Abstract

This thesis discusses one of the unified methods used to solve linear, non-linear equations, ordinary and partial differential equations known as the Adomian decomposition method. The Adomian decomposition method is discussed in details to include its background information, polynomials, convergence, formulation, boundary conditions, applications and advantages. Once the Adomian decomposition method has been thoroughly presented, its applications in systems of non-linear equations will be discussed in details and numerical examples will be provided to show the effectiveness of this method. Results of these numerical examples show that the Adomian decomposition method is an effective method to solve systems of non-linear equations with ease and favorable accuracy.