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Title: Underlying one-step methods and nonautonomous stability of general linear methods

Abstract

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. Here, 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.

Authors:
 [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Univ. of Kansas, Lawrence, KS (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
OSTI Identifier:
1467393
Report Number(s):
SAND-2018-3998J
Journal ID: ISSN 1553-524X; 662444
Grant/Contract Number:  
AC04-94AL85000; DMS-1419047
Resource Type:
Accepted Manuscript
Journal Name:
Discrete & Continuous Dynamical Systems - B
Additional Journal Information:
Journal Volume: 23; Journal Issue: 7; Journal ID: ISSN 1553-524X
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

J. Steyer, Andrew, and S. Van Vleck, Erik. Underlying one-step methods and nonautonomous stability of general linear methods. United States: N. p., 2018. Web. doi:10.3934/dcdsb.2018108.
J. Steyer, Andrew, & S. Van Vleck, Erik. Underlying one-step methods and nonautonomous stability of general linear methods. United States. doi:10.3934/dcdsb.2018108.
J. Steyer, Andrew, and S. Van Vleck, Erik. Sat . "Underlying one-step methods and nonautonomous stability of general linear methods". United States. doi:10.3934/dcdsb.2018108. https://www.osti.gov/servlets/purl/1467393.
@article{osti_1467393,
title = {Underlying one-step methods and nonautonomous stability of general linear methods},
author = {J. Steyer, Andrew and S. Van Vleck, Erik},
abstractNote = {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. Here, 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.},
doi = {10.3934/dcdsb.2018108},
journal = {Discrete & Continuous Dynamical Systems - B},
number = 7,
volume = 23,
place = {United States},
year = {2018},
month = {9}
}

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Cited by: 1 work
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