Stability analysis by quantifier elimination

Stanly Steinberg and Richard Liska

Mathematics and Computers in Simulation (MATCOM), 1996, vol. 42, issue 4, 629-638

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.

Keywords: Partial differential equations; Difference schemes; Stability; Quantifier elimination (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:42:y:1996:i:4:p:629-638

DOI: 10.1016/S0378-4754(96)00039-0

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