Strong-stability-preserving 3-stage Hermite-Birkhoff time-discretization methods

Authors:
Truong Nguyen-Ba;Huong Nguyen-Thu;Thierry Giordano;Rémi Vaillancourt
Affiliations:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada K1N 6N5;Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada K1N 6N5;Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada K1N 6N5;Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada K1N 6N5
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

Strong-stability-preserving (SSP) time-discretization methods have a nonlinear stability property that makes them particularly suitable for the integration of hyperbolic conservation laws. A collection of SSP explicit 3-stage Hermite-Birkhoff methods of orders 3 to 7 with nonnegative coefficients are constructed as k-step analogues of third-order Runge-Kutta methods, incorporating a function evaluation at two off-step points. Generally, these new methods have larger effective CFL coefficients than the hybrid methods of Huang with the same step number k. They have larger maximum scaled step sizes than hybrid methods on Burgers' equations.