Year: 2004
Author: Yan Xu, Chi-Wang Shu
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 2 : pp. 250–274
Abstract
In this paper, we further develop the local discontinuous Galerkin method to solve three classes of nonlinear wave equations formulated by the general KdV-Burgers type equations, the general fifth-order KdV type equations and the fully nonlinear $K(n, n, n)$ equations, and prove their stability for these general classes of nonlinear equations. The schemes we present extend the previous work of Yan and Shu [30, 31] and of Levy, Shu and Yan [24] on local discontinuous Galerkin method solving partial differential equations with higher spatial derivatives. Numerical examples for nonlinear problems are shown to illustrate the accuracy and capability of the methods. The numerical experiments include stationary solitons, soliton interactions and oscillatory solitary wave solutions. The numerical experiments also include the compacton solutions of a generalized fifth-order KdV equation in which the highest order derivative term is nonlinear and the fully nonlinear $K(n, n, n)$ equations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JCM-10327
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 2 : pp. 250–274
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Local discontinuous Galerkin method KdV-Burgers equation Fifth-order KdV equation Stability.