Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 195, Issue 25-28, Pages 3430-3447Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2005.06.021
Keywords
local discontinuous Galerkin method; Kuramoto-Sivashinsky equation; Ito-type coupled KdV equations; stability; exponential time differencing method
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In this paper we develop a local discontinuous Galerkin method to solve the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations. The L-2 stability of the schemes is obtained for both of these nonlinear equations. We use both the traditional nonlinearly stable explicit high order Runge-Kutta methods and the explicit exponential time differencing method for the time discretization; the latter can achieve high order accuracy and maintain good stability while avoiding the very restrictive explicit stability limit of the former when the PDE contains higher order spatial derivatives. Numerical examples are shown to demonstrate the accuracy and capability of these methods. (c) 2005 Elsevier B.V. All rights reserved.
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