Strong-stability-preserving, Hermite-Birkhoff time-discretization based on κ step methods and 8-stage explicit Runge-Kutta methods of order 5 and 4

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:263

Article

Huong Nguyen-Thu¹  Truong Nguyen-Ba²  Vaillancourt, Remi² 

[1] Cantho Univ, Sch Educ, Dept Math, Can Tho, Vietnam

[2] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada

关键词: Strong stability preserving;    Hermite-Birkhoff method;    SSP coefficient;    Time discretization.;    Method of lines;    Comparison with other SSP methods;   

DOI  :  10.1016/j.cam.2013.11.013

来源: Elsevier

【 摘 要 】

Ruuth and Spiteri have shown, in 2002, that fifth-order strong-stability-preserving (SSP) explicit Runge-Kutta (RK) methods with nonnegative coefficients do not exist. One of the purposes of the present paper is to show that the Ruuth-Spiteri barrier can be broken by adding backsteps to RK methods. New optimal, 8-stage, explicit, SSP, Hermite-Birkhoff (HB) time discretizations of order p, p = 5, 6,..., 12, with nonnegative coefficients are constructed by combining linear k-step methods of order (p 4) with an 8-stage explicit RK method of order 5 (RK(8, 5)). These new SSP HB methods preserve the monotonicity property of the solution and prevent error growth; therefore, they are suitable for solving hyperbolic partial differential equations (PDEs) by the method of lines. Moreover, these new HB methods have larger effective SSP coefficients and larger maximum effective CFL numbers than Huang's hybrid methods and RK methods of the same order when applied to the inviscid Burgers equation. Generally, HB methods combined with RK(8, 5) have maximum stepsize 24% larger than HB combined with RK(8, 4). (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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