On an accurate third order implicit-explicit Runge–Kutta method for stiff problems

Abstract

Most of the popular implicit-explicit (IMEX) Runge–Kutta (R-K) methods existing in the literature suffer from the phenomenon of order reduction in the stiff regime when applied to stiff problems containing a non-stiff term and a stiff term. Specifically, order reduction is observed when the problem becomes increasingly stiff. In this paper, our motivation is to derive a third-order IMEX R-K method for stiff problems that has a better temporal order of convergence than other well-known IMEX R-K methods. A comparison with other third-order methods shows substantial potential of this new method.