Functional-preserving predictor-corrector multiderivative schemes
arXiv:2308.04876 · doi:10.1002/pamm.202300025
Abstract
In this work, we develop a class of high-order multiderivative time integration methods that is able to preserve certain functionals discretely. Important ingredients are the recently developed Hermite-Birkhoff-Predictor-Corrector methods and the technique of relaxation for numerical methods of ODEs. We explain the algorithm in detail and show numerical results for two- and three-derivative methods, comparing relaxed and unrelaxed methods. The numerical results demonstrate that, at the slight cost of the relaxation, an improved scheme is obtained.
arXiv commentSubmitted to the Proceedings in Applied Mathematics and Mechanic (GAMM Annual Meeting 2023)
References in corpus (10)
- Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations
- High-order multiderivative time integrators for hyperbolic conservation laws
- General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes
- Relaxation Runge-Kutta Methods for Hamiltonian Problems
- Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations
- On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear Semibounded Operators
- A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations
- Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems
- A conservative fully-discrete numerical method for the regularised shallow water wave equations
- Two-derivative deferred correction time discretization for the discontinuous Galerkin method