STRONG STABILITY OF EXPLICIT RUNGE-KUTTA TIME DISCRETIZATIONS

被引：32

作者：

Sun, Zheng ^{[1
]}

Sho, Chi-Wang ^{[2
]}

机构：

[1] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA

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

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2019年 / 57卷 / 03期

基金：

美国国家科学基金会;

关键词：

Runge-Kutta methods; strong stability; energy method; hyperbolic problems; conditional contractivity; DISCONTINUOUS GALERKIN METHODS; FINITE-ELEMENT-METHOD; CONSERVATION-LAWS; FULLY-DISCRETE; SCHEMES; CONTRACTIVITY; SEMIDISCRETE; EQUATIONS; PAIRS;

D O I：

10.1137/18M122892X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Motivated by studies on fully discrete numerical schemes for linear hyperbolic conservation laws, we present a framework on analyzing the strong stability of explicit Runge-Kutta (RK) time discretizations for seminegative autonomous linear systems. The analysis is based on the energy method and can be performed with the aid of a computer. Strong stability of various RK methods, including a sixteen-stage embedded pair of order nine and eight, has been examined under this framework. Based on numerous numerical observations, we further characterize the features of strongly stable schemes. A both necessary and sufficient condition is given for the strong stability of RK methods of odd linear order.

引用

页码：1158 / 1182

页数：25

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