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2009, 2009(Special): 442-450. doi: 10.3934/proc.2009.2009.442

A dual-Petrov-Galerkin method for extended fifth-order Korteweg-de Vries type equations

Netra Khanal 1, , Ramjee Sharma 1, , Jiahong Wu 1, and  Juan-Ming Yuan 1,

1. 

Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, United States, United States, United States

Received  July 2008 Revised  March 2009 Published  September 2009

This paper extends the dual-Petrov-Galerkin method proposed by Shen [16] and further developed by Yuan, Shen and Wu [23] to several integrable and non-integrable fifth-order KdV type equations. These fifth-order equations arise in modeling different wave phenomena and involve various nonlinear terms. The method is implemented to compute the solitary wave solutions of these equations and the numerical results imply that this scheme is capable of capturing, with very high accuracy, the details of these solutions with modest computational costs. It is also shown that the scheme is stable under a very mild stability constraint, and is second-order accurate in time and spectrally accurate in space.
Keywords: Kaup-Kupershmidt equation, Lax equation, Solitary wave, Fifth-order KdV equation, Sawada-Kotera equation, Dual-Petrov-Galerkin, Spectral approximation.
Mathematics Subject Classification: Primary: 35Q53, 65M60; Secondary:65M60.
Citation: Netra Khanal, Ramjee Sharma, Jiahong Wu, Juan-Ming Yuan. A dual-Petrov-Galerkin method for extended fifth-order Korteweg-de Vries type equations. Conference Publications, 2009, 2009 (Special) : 442-450. doi: 10.3934/proc.2009.2009.442
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