Strong stability-preserving high-order time discretization methods

被引：1891

作者：

Gottlieb, S ^{[1
]}

Shu, CW

Tadmor, E

机构：

[1] Univ Massachusetts, Dept Math, Dartmouth, MA 02747 USA

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[3] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[4] NASA, Langley Res Ctr, ICASE, Hampton, VA 23681 USA

来源：

SIAM REVIEW | 2001年 / 43卷 / 01期

关键词：

strong stability preserving; Runge-Kutta methods; multistep methods; high-order accuracy; time discretization;

D O I：

10.1137/S003614450036757X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：89 / 112

页数：24