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Extrapolation-Based Super-Convergent Implicit-Explicit Peer Methods with A-stable Implicit Part

  • In this paper we extend the implicit-explicit (IMEX) methods of Peer type recently developed in [Lang, Hundsdorfer, J. Comp. Phys., 337:203–215, 2017] to a broader class of two-step methods that allow the construction of super- convergent IMEX-Peer methods with A-stable implicit part. IMEX schemes combine the necessary stability of implicit and low computational costs of ex- plicit 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 with favourable stability properties, we derive necessary and sufficient conditions on the coefficient matrices and apply an extrapolation approach based on already computed stage values. Optimised super-convergent IMEX-Peer methods of order s + 1 for s = 2, 3, 4 stages are given as result of a search algorithm carefully designed to balance the size of the stability regions and the extrapolation errors. Numerical experiments and a comparison to other IMEX-Peer methods are included.

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Metadaten
Author:Moritz Schneider, Jens Lang, Willem Hundsdorfer
DOI:https://doi.org/10.1016/j.jcp.2018.04.006
Document Type:Article
Language:English
Date of Publication (online):2017/11/26
Date of first Publication:2017/11/26
Release Date:2017/11/26
Volume:J. Comput. Physics
Issue:Vol. 367
Page Number:13
First Page:121
Last Page:133
Subprojects:B01