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.
Keywords
Citation
Inc, M. and Cherruault, Y. (2005), "A comparison of numerical solutions of fourth‐order boundary value problems", Kybernetes, Vol. 34 No. 7/8, pp. 960-968. https://doi.org/10.1108/03684920510605786
Publisher
:Emerald Group Publishing Limited
Copyright © 2005, Emerald Group Publishing Limited