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Super-Convergent Implicit-Explicit Peer Methods with Variable Step Sizes

  • Dynamical systems with sub-processes evolving on many different time scales are ubiquitous in applications. Their efficient solution is greatly enhanced by automatic time step variation. This paper is concerned with the theory, construction and application of IMEX-Peer methods that are super-convergent for variable step sizes and A-stable in the implicit part. IMEX schemes combine the necessary stability of implicit and low computational costs of explicit methods to efficiently solve systems of ordinary differential equations with both stiff and non-stiff parts included in the source term. To construct super-convergent IMEX-Peer methods which keep their higher order for variable step sizes and exhibit favourable linear stability properties, we derive necessary and sufficient conditions on the nodes and coefficient matrices and apply an extrapolation approach based on already computed stage values. New super-convergent IMEX-Peer methods of order s + 1 for s = 2, 3, 4 stages are given as result of additional order conditions which maintain the super-convergence property independent of step size changes. Numerical experiments and a comparison to other super-convergent IMEX-Peer methods show the potential of the new methods when applied with local error control.

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Author:Moritz Schneider, Jens Lang, Rüdiger Weiner
DOI:https://doi.org/doi:10.1016/j.cam.2019.112501
Document Type:Article
Language:English
Date of Publication (online):2019/02/04
Date of first Publication:2019/03/26
Release Date:2019/03/26
Volume:J. Comput. Appl. Math.
Issue:387
First Page:112501
Institutes:Technische Universität Darmstadt
Subprojects:B01
Licence (German):License LogoCreative Commons - CC BY-ND - Namensnennung - Keine Bearbeitungen 4.0 International