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

M. Inc (Department of Mathematics, Firat University, Elazig, Turkey)
Y. Cherruault (Laboratoire MEDIMAT, Université Pierre et Marie Curie, Paris, France)

Kybernetes

ISSN: 0368-492X

Article publication date: 1 August 2005

369

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

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