Strong-Stability-Preserving 7-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, Canada K1N 6N5;Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada K1N 6N5;Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada K1N 6N5;Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada K1N 6N5
Venue:
Journal of Scientific Computing
Year:
2012

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Abstract

Optimal, 7-stage, explicit, strong-stability-preserving (SSP) Hermite---Birkhoff (HB) methods of orders 4 to 8 with nonnegative coefficients are constructed by combining linear k-step methods with a 7-stage Runge---Kutta (RK) method of order 4. Compared to Huang's hybrid methods of the same order, the new methods generally have larger effective SSP coefficients and larger maximum effective CFL numbers, $\text{num}_{\text{eff}}$ , on Burgers' equation, independently of the number k of steps, especially when k is small for both methods. Based on $\text{num}_{\text{eff}}$ , some new methods of order 4 compare favorably with other methods of the same order, including RK104 of Ketcheson. The new SSP HB methods are listed in their Shu---Osher representation in Appendix.