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Solving Stability Problems Using Quantifier Elimination

  • Richard Liska
  • Stanly Steinberg
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 121)

Abstract

Stability problems for initial-value problems for partial differential equations and their discretizations can be written as quantifier elimination problems. Such problems can be solved by general quantifier elimination algorithms. However, if is far more efficient to use the Routh-Hurwitz or related criteria to eliminate one of the quantified variables before the general algorithms are applied.

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References

  1. [1]
    C. Abdallah, P. Dorato, R. Liska, S. Steinberg, and W. Yang, Applications of Quantifier Elimination to Problems in Control Theory, Submitted to IFAC Congress, 1996.Google Scholar
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    G.E. Collins and H. Hong, Partial cylindrical algebraic decomposition for quantifier elimination, J. Symb. Comp., 12 (1991), 299–328.MathSciNetzbMATHCrossRefGoogle Scholar
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    H.-O. Kreiss and J. Lorenz, Initial-Boundary Value Problems and the Navier-Stokes Equations Academic Press, Boston, 1989.Google Scholar
  4. [4]
    R. Liska and S. Steinberg, Using Quantifier Elimination to Test Stability submitted to the special issue of Journal of Symbolic Computation on Quantifier Elimination and its Applications.Google Scholar
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    J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Wadsworth, Inc., Belmont, 1989.Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1996

Authors and Affiliations

  • Richard Liska
    • 1
  • Stanly Steinberg
    • 2
  1. 1.Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PraguePrague 1Czech Republic
  2. 2.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA

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