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A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-29
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
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 ∞ 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.
American Psychological Association (APA)
Momoniat, Ebrahim. 2014. A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-14.
https://search.emarefa.net/detail/BIM-1014730
Modern Language Association (MLA)
Momoniat, Ebrahim. A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation. Abstract and Applied Analysis No. 2014 (2014), pp.1-14.
https://search.emarefa.net/detail/BIM-1014730
American Medical Association (AMA)
Momoniat, Ebrahim. A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-14.
https://search.emarefa.net/detail/BIM-1014730
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014730