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：我们将近期提出的松弛方法与多导数龙格-库塔方法相结合，以保持常微分方程和偏微分方程中熵泛函的守恒性或耗散性。松弛方法是对显式和隐式格式的微调，除了基准方案外，每个时间步仅需求解一个标量方程。我们通过一系列测试问题（包括三维可压缩欧拉方程）展示了所提方法的鲁棒性。特别地，我们指出对于某些熵守恒问题（包括非线性色散波动方程），误差增长率得到了改善。