We note a fact that stiff systems or differential equations that have highly oscillatory solutions cannot be solved efficiently using conventional methods. In this paper, 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：本文注意到一个事实：传统方法无法高效求解具有高频振荡解的刚性系统或微分方程。本文研究了两类新型指数龙格-库塔（ERK）积分器，用于高效求解刚性系统或高频振荡问题。我们首先基于阶条件提出一类新型显式修正型指数龙格-库塔（MVERK）方法。此外，我们还考虑了一类显式简化型指数龙格-库塔（SVERK）方法。数值结果表明，与文献中著名的显式ERK积分器相比，本文推导的显式MVERK积分器和SVERK方法在求解刚性系统或高频振荡问题时具有显著的高效性。