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FOURTH-ORDER NUMERICAL METHODS FOR THE COUPLED KORTEWEG–DE VRIES EQUATIONS

Part of: Equations of mathematical physics and other areas of application Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  16 March 2015

I. A. KOROSTIL  and
S. R. CLARKE
I. A. KOROSTIL*
Affiliation:
The Kirby Institute, University of New South Wales, Sydney, Australia email [email protected]
S. R. CLARKE
Affiliation:
School of Mathematical Sciences, Monash University, Melbourne, Australia email [email protected]
*
✉[email protected]
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Abstract

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We compare six fixed-stepsize fourth-order numerical methods for a number of test problems described by a system of coupled Korteweg–de Vries equations. Particular attention is paid to the ability of these methods to preserve fixed points (solitary waves) and the invariants of the system, and establishing to what extent the conservation of integral invariants is indicative of the solution error for these methods.

Keywords

coupled Korteweg–de Vries equationsnumerical methodsexponential integratorsimplicit Runge–Kutta method

MSC classification

Primary: 35Q53: KdV-like equations (Korteweg-de Vries)
Secondary: 65M70: Spectral, collocation and related methods
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 3 , January 2015 , pp. 275 - 285
Copyright
© 2015 Australian Mathematical Society 

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