The Numerical Solution of Special Fourth-Order Boundary Value Problems by the Modified Decomposition Method

Abstract

In this paper we develop a fast and accurate algorithm for the solution of special fourth-order boundary value problems with two-point boundary conditions. A modified form of the Adomian decomposition method is applied to construct the numerical solution for such problems. The new approach has two distinct features (i) it provides the solution in a rapidly convergent series, and (ii) it also requires less computational effort. The scheme is tested on two linear and nonlinear problems. The obtained results demonstrate reliability of the algorithm.