Multiderivative time integration methods preserving nonlinear functionals via relaxation

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.