New Paper published: 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 for non-uniformly refined meshes and spatially varying 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. These methods are constructed to reduce the amplification of round off errors which becomes a significant concern for these many-stage methods.

Published in Springer Journal of Scientific Computing

Authors: Daniel Doehring, Gregor Gassner, Manuel Torrilhon


DOI: doi:10.1007/s10915-024-02478-5

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