We combine the recent relaxation approach with multiderivative Runge-Kutta methods to preserve conservation or dissipation of entropy functionals for ordinary and partial differential equations. Relaxation methods are minor modifications of explicit and implicit schemes, requiring only the solution of a single scalar equation per time step in addition to the baseline scheme. We demonstrate the robustness of the resulting methods for a range of test problems including the 3D compressible Euler equations. In particular, we point out improved error growth rates for certain entropy-conservative problems including nonlinear dispersive wave equations.

翻译：我们将最新的松弛方法与多导数龙格-库塔法结合，以保持常微分方程和偏微分方程中熵泛函的守恒或耗散性。松弛法是对显式和隐式格式的微小修改，除基础方案外，每个时间步仅需求解单个标量方程。我们通过一系列测试问题（包括三维可压缩欧拉方程）证明了所得方法的稳健性。特别地，对于某些熵守恒问题（包括非线性色散波方程），我们指出了改进的误差增长率。