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The Computer Journal 1993 36(5):497-503; doi:10.1093/comjnl/36.5.497
© 1993 by British Computer Society
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Applying Quantifier Elimination to Stability Analysis of Difference Schemes

R. Liska1 * and S. Steinberg2 §

1 Teikyo University of Technology, Uruido, Ichihara, Chiba 290-01, Japan, 2 Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM, USA

Stability analysis is an important tool for constructing time-stepping finite difference schemes for partial differential equations. This paper describes how von Neumann stability analysis can be reduced to a quantifier elimination problem over the reals. We report our experience in analysing some difference schemes by using a quantifier package based on the partial cylindrical algebraic decomposition algorithm.

Received January 1993. revised May 1993.

* Teikyo University of Technology, Uruido, Ichihara, Chiba 290-01, Japan

§ Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM, USA


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