UNDERLYING ONE-STEP METHODS AND NONAUTONOMOUS STABILITY OF GENERAL LINEAR METHODS

被引：1
|
作者：
Steyer, Andrew J. [1 ]
Van Vleck, Erik S. [2 ]
机构：
[1] Sandia Natl Labs, POB 5800,MS 1320, Albuquerque, NM 87185 USA
[2] Univ Kansas, Dept Math, 1460 Jayhawk Blvd, Lawrence, KS 66045 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2018年 / 23卷 / 07期
基金：
美国国家科学基金会;
关键词：
General linear method; underlying one-step method; nonautonomous; Lyapunov exponents; Lyapunov exponent; Sacker-Sell spectrum; DIFFERENTIAL-EQUATIONS; MULTISTEP METHODS; CONJUGATE-SYMPLECTICITY; SPECTRAL INTERVALS; LYAPUNOV EXPONENTS; INVARIANT CURVES; SYSTEMS; COMPUTATION; ATTRACTORS;
D O I：
10.3934/dcdsb.2018108
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We generalize the theory of underlying one-step methods to strictly stable general linear methods (GLMs) solving nonautonomous ordinary differential equations (ODEs) that satisfy a global Lipschitz condition. We combine this theory with the Lyapunov and Sacker-Sell spectral stability theory for one-step methods developed in [34, 35, 36] to analyze the stability of a strictly stable GLM solving a nonautonomous linear ODE. These results are applied to develop a stability diagnostic for the solution of nonautonomous linear ODEs by strictly stable GLMs.
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页码：2859 / 2877
页数：19
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