Symmetric hyperbolic difference schemes and matrix problems |
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Authors: | E Turkel |
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Institution: | Courant Institute of Mathematical Sciences New York University New York, New York 10012, USA |
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Abstract: | Sufficient conditions for the stability of multidimensional finite difference schemes are difficult to obtain. It is shown that for special families of amplification matrices G (A, B) a sufficient condition for power boundedness can be obtained by replacing the matrices by appropriate scalars, and so the problem is reduced to a scalar one. As one application it is shown that the Lax-Wendroff scheme in two dimensions is stable if |Au| + |Bu| ? 1 for all real unit vectors u. The Lax- Wendroff scheme with stabilizer does not always permit such large time steps. It is conjectured that the analysis for all symmetric hyperbolic schemes can be reduced to the scalar case. |
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