Stability analysis by quantifier elimination Original Research Article

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.