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
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
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页码:1158 / 1182
页数:25
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