Strong stability-preserving high-order time discretization methods
Strong stability-preserving high-order time discretization methods
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DOI：
10.1137/s003614450036757x
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发表时间：
2001-03-01
期刊：
影响因子：
10.2
通讯作者：
Tadmor, E
中科院分区：
文献类型：
--
作者：
Gottlieb, S;Shu, CW;Tadmor, E
本文讨论并发展了偏微分方程半离散线逼近的一类强保稳定高阶时间离散格式。以前称为TVD（总变差递减）时间离散，这些高阶时间离散方法保持了一阶欧拉时间步进的强稳定性，并已被证明是非常有用的，特别是在求解双曲型偏微分方程。本文的新进展包括最优显式SSP线性Runge-Kutta方法的构造、它们在强制逼近强稳定性中的应用、非线性问题显式SSP多步法的系统研究以及隐式Runge-Kutta和多步法的SSP性质的研究。
In this paper we review and further develop a class of strong stability-preserving (SSP) high-order time discretizations for semidiscrete method of lines approximations of partial differential equations. Previously termed TVD (total variation diminishing) time discretizations, these high-order time discretization methods preserve the strong stability properties of first-order Euler time stepping and have proved very useful, especially in solving hyperbolic partial differential equations. The new developments in this paper include the construction of optimal explicit SSP linear Runge-Kutta methods, their application to the strong stability of coercive approximations, a systematic study of explicit SSP multistep methods for nonlinear problems, and the study of the SSP property of implicit Runge-Kutta and multistep methods.