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Optimal Rate of Convergence for a Nonstandard Finite Difference Galerkin Method Applied to Wave Equation Problems
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-12-30
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
The optimal rate of convergence of the wave equation in both the energy and the L2-norms using continuous Galerkin method is well known.
We exploit this technique and design a fully discrete scheme consisting of coupling the nonstandard finite difference method in the time and the continuous Galerkin method in the space variables.
We show that, for sufficiently smooth solution, the maximal error in the L2-norm possesses the optimal rate of convergence O(h2+(Δt)2) where h is the mesh size and Δt is the time step size.
Furthermore, we show that this scheme replicates the properties of the exact solution of the wave equation.
Some numerical experiments should be performed to support our theoretical analysis.
American Psychological Association (APA)
Chin, Pius W. M.. 2013. Optimal Rate of Convergence for a Nonstandard Finite Difference Galerkin Method Applied to Wave Equation Problems. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-478236
Modern Language Association (MLA)
Chin, Pius W. M.. Optimal Rate of Convergence for a Nonstandard Finite Difference Galerkin Method Applied to Wave Equation Problems. Journal of Applied Mathematics No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-478236
American Medical Association (AMA)
Chin, Pius W. M.. Optimal Rate of Convergence for a Nonstandard Finite Difference Galerkin Method Applied to Wave Equation Problems. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-478236
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-478236