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2014 A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation
E. Momoniat
Abstr. Appl. Anal. 2014(SI37): 1-14 (2014). DOI: 10.1155/2014/754543

Abstract

Two nonstandard finite difference schemes are derived to solve the regularized long wave equation. The criteria for choosing the “best” nonstandard approximation to the nonlinear term in the regularized long wave equation come from considering the modified equation. The two “best” nonstandard numerical schemes are shown to preserve conserved quantities when compared to an implicit scheme in which the nonlinear term is approximated in the usual way. Comparisons to the single solitary wave solution show significantly better results, measured in the L2 and L norms, when compared to results obtained using a Petrov-Galerkin finite element method and a splitted quadratic B-spline collocation method. The growth in the error when simulating the single solitary wave solution using the two “best” nonstandard numerical schemes is shown to be linear implying the nonstandard finite difference schemes are conservative. The formation of an undular bore for both steep and shallow initial profiles is captured without the formation of numerical instabilities.

Citation

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E. Momoniat. "A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation." Abstr. Appl. Anal. 2014 (SI37) 1 - 14, 2014. https://doi.org/10.1155/2014/754543

Information

Published: 2014
First available in Project Euclid: 6 October 2014

zbMATH: 07023022
MathSciNet: MR3206819
Digital Object Identifier: 10.1155/2014/754543

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI37 • 2014
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