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arXiv · 1610.00518

Extrapolation-Based Implicit-Explicit Peer Methods with Optimised Stability Regions

Jens Lang·Willem Hundsdorfer
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Abstract

In this paper we investigate a new class of implicit-explicit (IMEX) two-step methods of Peer type for systems of ordinary differential equations with both non-stiff and stiff parts included in the source term. An extrapolation approach based on already computed stage values is applied to construct IMEX methods with favourable stability properties. Optimised IMEX-Peer methods of order p = 2, 3, 4, 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 implicit-explicit methods are included.

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Jens Lang, Willem Hundsdorfer. 2016-10-03. Extrapolation-Based Implicit-Explicit Peer Methods with Optimised Stability Regions. https://doi.org/10.1016/j.jcp.2017.02.034

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