04-03
On stability of the evolution Galerkin schemes applied to a two-dimensional wave equation system
by Lukacova-Medvidova, M.; Warnecke, G.; Zahaykah, Y.
Preprint series: 04-03, Preprints
- MSC:
- 35L05 Wave equation
- 65M06 Finite difference methods
- 35L45 Initial value problems for hyperbolic systems of first-order PDE
- 35L65 Conservation laws
- 65M25 Method of characteristics
- 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
- 65M12 Stability and convergence of numerical methods
Abstract: The subject of the paper is the analysis of stability of the evolution Galerkin (EG) methods for the two-dimensional wave equation system. We apply von Neumann analysis and use the Fourier transformation to estimate the stability limits of both the first and the second order EG methods.
Keywords: hyberbolic systems, wave equation, evolution Galerkin schemes, discrete Fourier transformation, amplification matrix, CFL condition.
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