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On stability of the evolution Galerkin schemes applied to a two-dimensional wave equation system

by Lukacova-Medvidova, M., Warnecke, G., Zahaykah, Y..

Series: 2004-03, Preprints

35L05 Wave equation
65M06 Finite difference methods
35L45 Initial value problems for first-order hyperbolic systems
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

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.

hyberbolic systems, wave equation, evolution Galerkin schemes, discrete Fourier transformation, amplification matrix, CFL condition.