New Paper ‘Multiderivative time integration methods preserving nonlinear functionals via relaxation’ published in Communications in Applied Mathematics and Computational Science

The paper Multiderivative time integration methods preserving nonlinear functionals via relaxation of Jochen Schütz and me has been published in Communications in Applied Mathematics and Computational Science.

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.

The reproducibility repository is available on GitHub.

As usual, you can find the preprint on arXiv.