Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations
Abstract
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.
Cite
@article{arxiv.2402.12140,
title = {Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations},
author = {Daniel Doehring and Gregor J. Gassner and Manuel Torrilhon},
journal= {arXiv preprint arXiv:2402.12140},
year = {2024}
}