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.
