Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations
<|reference_start|>Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations: A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta methods is devised. Intended for semidiscretizations of hyperbolic partial differential equations, the herein developed approach allows the optimization of stability polynomials with more than hundred stages. A potential application of these high degree stability polynomials are problems with locally varying characteristic speeds as found in non-uniformly refined meshes and different wave speeds.   To demonstrate the applicability of the stability polynomials we construct 2N storage many-stage Runge-Kutta methods that match their designed second order of accuracy when applied to a range of linear and nonlinear hyperbolic PDEs with smooth solutions. The methods are constructed to reduce the amplification of round off errors which becomes a significant concern for these many-stage methods.<|reference_end|>
@article{doehring2024many-stage,
    title={Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial
  Differential Equations},
    author={Daniel Doehring, Gregor J. Gassner, Manuel Torrilhon},
    journal={arXiv preprint arXiv:2402.12140},
    year={2024},
    doi={10.1007/s10915-024-02478-5},
    archivePrefix={arXiv},
    eprint={2402.12140},
    primaryClass={math.NA cs.NA math-ph math.CA math.MP}
}