We study two new classes of exponential Runge-Kutta (ERK) integrators for efficiently solving stiff systems or highly oscillatory problems. We first present a novel class of explicit modified version of exponential Runge-Kutta (MVERK) methods based on the order conditions. Furthermore, we consider a class of explicit simplified version of exponential Runge-Kutta (SVERK) methods. Numerical results demonstrate the high efficiency of the explicit MVERK integrators and SVERK methods derived in this paper compared with the well-known explicit ERK integrators for stiff systems or highly oscillatory problems in the literature.

翻译：我们研究两种新型的指数龙格-库塔(ERK)集成器,以有效解决僵硬系统或高度悬浮问题。我们首先展示了一种新型的基于定序条件的指数龙格-库塔(MVERK)方法的明确修改版本。此外,我们考虑了一种指数龙格-库塔(SVERK)方法的明确简化版本。数字结果表明,与文献中众所周知的僵硬系统或高度悬浮问题明显的ERK集成器相比,本文中生成的显性MVERK集成器和SVERK方法的效率很高。