Strong Stability Preserving Runge–Kutta and Linear Multistep Methods

被引：0
作者：
Giuseppe Izzo
Zdzislaw Jackiewicz
机构：
[1] Università di Napoli Federico II,Dipartimento di Matematica e Applicazioni
[2] Arizona State University,School of Mathematical and Statistical Sciences
来源：
Bulletin of the Iranian Mathematical Society | 2022年 / 48卷 / 6期
关键词：
Runge–Kutta methods; Linear multistep methods; General linear methods; Monotonicity; Strong stability preserving; SSP coefficient; Shu–Osher representation; 65Lxx; 65L05; 65L06;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper reviews strong stability preserving discrete variable methods for differential systems. The strong stability preserving Runge–Kutta methods have been usually investigated in the literature on the subject, using the so-called Shu–Osher representation of these methods, as a convex combination of first-order steps by forward Euler method. In this paper, we revisit the analysis of strong stability preserving Runge–Kutta methods by reformulating these methods as a subclass of general linear methods for ordinary differential equations, and then using a characterization of monotone general linear methods, which was derived by Spijker in his seminal paper (SIAM J Numer Anal 45:1226–1245, 2007). Using this new approach, explicit and implicit strong stability preserving Runge–Kutta methods up to the order four are derived. These methods are equivalent to explicit and implicit RK methods obtained using Shu–Osher or generalized Shu–Osher representation. We also investigate strong stability preserving linear multistep methods using again monotonicity theory of Spijker.
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页码：4029 / 4062
页数：33
相关论文
共 46 条
  • [11] Ferracina L(2005)On monotonicity and boundedness properties of linear multistep methods Math. Comput. 75 655-672
  • [12] Spijker MN(2015)Strong stability preserving general linear methods J. Sci. Comput. 65 271-298
  • [13] Ferracina L(2015)Strong stability preserving multistage integration methods Math. Model. Anal. 20 552-577
  • [14] Spijker MN(2018)Strong stability preserving transformed DIMSIMs J. Comput. Appl. Math. 343 174-188
  • [15] Gottlieb S(2009)Computation of optimal monotonicity preserving general linear methods Math. Comput. 78 1497-1513
  • [16] Shu C-W(2011)Strong stability preserving two-step Runge–Kutta methods SIAM J. Numer. Anal. 49 2618-2639
  • [17] Gottlieb S(2009)Optimal implicit strong stability preserving Runge–Kutta methods Appl. Numer. Math. 59 373-392
  • [18] Shu C-W(2018)Strong stability preserving explicit peer methods for discontinuous Galerkin discretizations J. Sci. Comput. 75 1057-1078
  • [19] Tadmor E(1991)Contractivity of Runge–Kutta methods BIT 31 482-528
  • [20] Higueras I(1989)Contractivity-preserving explicit linear multistep methods Numer. Math. 55 213-223
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