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Stability analysis by quantifier elimination

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  • Steinberg, Stanly
  • Liska, Richard

Abstract

Stability is one of the important properties of time-stepping numerical schemes that are used to approximate partial differential equations. Stability can be analyzed using Von Neumann stability analysis which is a Fourier method. The analysis results in the Von Neumann stability condition which is transformed into a set of universally quantified polynomial inequalities. The universally quantified variables are eliminated by the quantifier elimination using the cylindrical algebraic decomposition algorithm. The resulting stability condition is a set of analytic inequalities which place constraints on the parameters of the numerical scheme. All the stages of the analysis are done using symbolic computation.

Suggested Citation

  • Steinberg, Stanly & Liska, Richard, 1996. "Stability analysis by quantifier elimination," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 42(4), pages 629-638.
    • Handle: RePEc:eee:matcom:v:42:y:1996:i:4:p:629-638
    DOI: 10.1016/S0378-4754(96)00039-0
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    Cited by:

    1. Banshchikov, Andrej & Bourlakova, Larissa, 2001. "Computer algebra and problems of motion stability," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(3), pages 161-174.

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