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We note a fact that stiff systems or differential equations that have highlyoscillatory 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 oscillatoryproblems. We first present a novel class of explicit modified version ofexponential Runge-Kutta (MVERK) methods based on the order conditions.Furthermore, we consider a class of explicit simplified version of exponentialRunge-Kutta (SVERK) methods. Numerical results demonstrate the high efficiencyof the explicit MVERK integrators and SVERK methods derived in this papercompared with the well-known explicit ERK integrators for stiff systems orhighly oscillatory problems in the literature.

Two new classes of exponential Runge-Kutta integrators for efficiently solving stiff systems or highly oscillatory problems