A modified equation approach to selecting a nonstandard finite difference scheme applied to the regularized long wave equation
type: Item
instance of: scholarly article
title: A modified equation approach to selecting a nonstandard finite difference scheme applied to the regularized long wave equation
zbMATH Open document ID: 1474.65285
DOI: 10.1155/2014/754543
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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 \(L_2\) and \(L_\infty\) 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.
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 7023022
Wikidata QID: Q59041255
author: E. Momoniat
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/754543
OpenAlex ID: W1999982254
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description: scientific article; zbMATH DE number 7023022