TY - JOUR A1 - Lang, Jens A1 - Hundsdorfer, Willem T1 - Extrapolation-based implicit–explicit Peer methods with optimised stability regions N2 - 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. Y1 - 2017 U6 - https://doi.org/doi:10.1016/j.jcp.2017.02.034 VL - J. Comput. Phys. IS - 337 SP - 203 EP - 215 ER - TY - JOUR A1 - Schneider, Moritz A1 - Lang, Jens A1 - Hundsdorfer, Willem T1 - Extrapolation-Based Super-Convergent Implicit-Explicit Peer Methods with A-stable Implicit Part N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1016/j.jcp.2018.04.006 VL - J. Comput. Physics IS - Vol. 367 SP - 121 EP - 133 ER -