Two new classes of exponential Runge-Kutta integrators for efficiently solving stiff systems or highly oscillatory problems
Abstract
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.
Cite
@article{arxiv.2210.00685,
title = {Two new classes of exponential Runge-Kutta integrators for efficiently solving stiff systems or highly oscillatory problems},
author = {Bin Wang and Xianfa Hu and Xinyuan Wu},
journal= {arXiv preprint arXiv:2210.00685},
year = {2023}
}