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Abstract and Applied Analysis
Volume 2014, Article ID 438289, 11 pages
http://dx.doi.org/10.1155/2014/438289
Research Article

A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation

1Center for Computational Geosciences, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
2Department of Chemical & Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB, Canada T2N 1N4

Received 26 March 2014; Accepted 31 May 2014; Published 19 June 2014

Academic Editor: Ljubisa Kocinac

Copyright © 2014 Liquan Mei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. A Fourier stability analysis for the method is shown to be marginally stable. Three invariants of motion are investigated. Numerical experiments are presented to check the theoretical study of this method.