A dual-Petrov-Galerkin method for extended fifth-order Korteweg-de Vries type equations
Netra Khanal - Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, United States (email)
Abstract: This paper extends the dual-Petrov-Galerkin method proposed by Shen  and further developed by Yuan, Shen and Wu  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: Dual-Petrov-Galerkin, Fifth-order KdV equation, Kaup-Kupershmidt equation, Lax equation, Sawada-Kotera equation, Spectral approximation, Solitary wave
Received: July 2008; Revised: March 2009; Published: September 2009.