467 RWTH Publication No: 696211        2017        IGPM467.pdf
TITLE Asymptotic Error Analysis of an IMEX Runge-Kutta method
AUTHORS Klaus Kaiser, Jochen Schütz
ABSTRACT We consider a system of singularly perturbed differential equations with singular parameter ε<<1, discretized with an IMEX Runge-Kutta method. The splitting needed for the IMEX method stems from a linearization of the fluxes around the limit solution. We analyze the asymptotic convergence order as ε→0. We show that in this setting, the minimal stage order of the implicit part of the scheme is of great importance, thereby explaining earlier numerical results showing a close correlation of errors of the splitting scheme and the fully implicit one.
KEYWORDS Order reduction, RS-IMEX, IMEX Runge-Kutta, singularly perturbed equation, asymptotic convergence order
DOI 10.1016/j.cam.2018.04.044
PUBLICATION Journal of Computational and Applied Mathematics, Volume 343, 1 December 2018, Pages 139-154