A comparison of numerical solutions of fourth-order boundary value problems

Abstract

Purpose - To use the modified decomposition method to obtain numerical solutions of fourth-order boundary value problems. Design/methodology/approach - The modified form of Adomian decomposition method (ADM) originated by Wazwaz in 1997/1998 is considered and applied. In addition, a comparison of the modified decomposition method and the perturbed collocation method when applied to the solutions of fourth-order boundary value problems is presented. Findings - The comparison of these two methods has shown that the modified or standard decomposition methods are reliable, efficient and easy to use for solving higher-order boundary value problems. Research limitations/implications - This study provides both an analysis of the method as well as a comparison of the numerical solutions of fourth-order boundary value problems. Future research in the application of this methodology to other areas should prove productive. Practical implications - The numerical results, using the modified technique, were obtained from selected fourth-order boundary value problems which were linear and non-linear problems. Originality/value - Assesses, by comparison, methods for the numerical solutions of fourth-order boundary value problems. Shows through original numerical results the value of the modified or standard decomposition methods in the solution of these problems.