Stability of linear multistep methods and applications to nonlinear parabolic problems

Authors:
A. Ostermann;M. Thalhammer;G. Kirlinger
Affiliations:
Institut für Technische Mathematik, Geometrie und Bauinformatik, Universität Innsbruck, Technikerstraße 13, A.6020 Innsbruck, Austria;Institut für Technische Mathematik, Geometrie und Bauinformatik, Universität Innsbruck, Technikerstraße 13, A.6020 Innsbruck, Austria;Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Wiedner Hauptstraße 8-10/115, A-1040 Wien, Austria
Venue:
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Year:
2004

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Abstract

In the present paper, stability and convergence properties of linear multistep methods are investigated. The attention is focused on parabolic problems and variable stepsizes. Under weak assumptions on the method and the stepsize sequence an asymptotic stability result is shown. Further, stability bounds for linear nonautonomous parabolic problems with Hölder continuous operator are given. With the help of these results, convergence estimates for semilinear and fully nonlinear parabolic problems are derived.