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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada, K1N 6N5

    Truong Nguyen-Ba, Huong Nguyen-Thu, Thierry Giordano & Rémi Vaillancourt

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  1. Truong Nguyen-Ba
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  2. Huong Nguyen-Thu
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  3. Thierry Giordano
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  4. Rémi Vaillancourt
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Correspondence to Rémi Vaillancourt.

Additional information

This work was supported in part by the Vietnam Ministry of Education and Training, the Natural Sciences and Engineering Research Council of Canada and the Centre de recherches mathématiques of the Université de Montréal.

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Nguyen-Ba, T., Nguyen-Thu, H., Giordano, T. et al. Strong-Stability-Preserving 7-Stage Hermite–Birkhoff Time-Discretization Methods. J Sci Comput 50, 63–90 (2012). https://doi.org/10.1007/s10915-011-9473-7

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  • DOI: https://doi.org/10.1007/s10915-011-9473-7

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