Strong-Stability-Preserving 7-Stage Hermite–Birkhoff Time-Discretization Methods

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...

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Bibliographic Details
Published in:Journal of scientific computing 2012, Vol.50 (1), p.63-90
Main Authors: Nguyen-Ba, Truong, Nguyen-Thu, Huong, Giordano, Thierry, Vaillancourt, Rémi
Format: Article
Language:English
Subjects:
Algorithms
Burgers equation
Computational Mathematics and Numerical Analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Runge-Kutta method
Stability
Theoretical
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Summary: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, , on Burgers’ equation, independently of the number k of steps, especially when k is small for both methods. Based on , 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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-011-9473-7