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

摘要

In this paper we extend the implicit-explicit (IMEX) methods of Peer typerecently developed in [Lang, Hundsdorfer, J. Comp. Phys., 337:203--215, 2017]to a broader class of two-step methods that allow the construction ofsuper-convergent IMEX-Peer methods with A-stable implicit part. IMEX schemescombine the necessary stability of implicit and low computational costs ofexplicit methods to efficiently solve systems of ordinary differentialequations with both stiff and non-stiff parts included in the source term. Toconstruct super-convergent IMEX-Peer methods with favourable stabilityproperties, we derive necessary and sufficient conditions on the coefficientmatrices and apply an extrapolation approach based on already computed stagevalues. Optimised super-convergent IMEX-Peer methods of order s+1 for s=2,3,4stages are given as result of a search algorithm carefully designed to balancethe size of the stability regions and the extrapolation errors. Numericalexperiments and a comparison to other IMEX-Peer methods are included.