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On the solution of the non‐linear Korteweg–de Vries equation by the decomposition method

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

Kybernetes

ISSN: 0368-492X

Article publication date: 1 July 2002

Abstract

The Adomian decomposition method is used to implement the non‐linear Korteweg–de Vries equations. The analytic solution of the equation is calculated in the form of a convergent power series with easily computable components. The non‐homogeneous problem is quickly solved by observing the self‐cancelling “noise” terms whose sum vanishes in the limit. Comparing this methodology with some known techniques shows that the present approach is highly accurate.

Keywords

Citation

Cherruault, Y., Inc, M. and Abbaoui, K. (2002), "On the solution of the non‐linear Korteweg–de Vries equation by the decomposition method", Kybernetes, Vol. 31 No. 5, pp. 766-772. https://doi.org/10.1108/03684920210428263

Publisher

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MCB UP Ltd

Copyright © 2002, MCB UP Limited