Reformulated Adomian Decomposition Method for the Approximation of Special Linear and Nonlinear Two-Point Boundary Value Problems

Abstract

Boundary value problems (BVPs) of higher order have been found to be potentially applicable in hydro-magnetic stability, hydrodynamics, chemical reactions, heat power transmission theory, and the boundary layer theory in fluid mechanics. In this research, a method which decomposes the solution into the series which converges rapidly shall be derived. We shall call this method the reformulated Adomian decomposition method (RADM). This method is an improvement over Aadomian decomposition method (ADM). The RADM is derived in such a way that on imposing the boundary conditions on the approximant, a system of equations is obtained which in turn is solved for the undetermined constants. On substituting the resulting constants into the solution function, we obtain a series solution to the problem. The RADM is applied on some linear and nonlinear two-point BVPs and from the results obtained, the method is said to be computationally reliable.