Underlying onestep methods and nonautonomous stability of general linear methods
Abstract
We generalize the theory of underlying onestep 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 SackerSell spectral stability theory for onestep 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:

 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Univ. of Kansas, Lawrence, KS (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
 OSTI Identifier:
 1467393
 Report Number(s):
 SAND20183998J
Journal ID: ISSN 1553524X; 662444
 Grant/Contract Number:
 AC0494AL85000; DMS1419047
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Discrete & Continuous Dynamical Systems  B
 Additional Journal Information:
 Journal Volume: 23; Journal Issue: 7; Journal ID: ISSN 1553524X
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
Citation Formats
J. Steyer, Andrew, and S. Van Vleck, Erik. Underlying onestep 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 onestep 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 onestep 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 onestep methods and nonautonomous stability of general linear methods},
author = {J. Steyer, Andrew and S. Van Vleck, Erik},
abstractNote = {We generalize the theory of underlying onestep 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 SackerSell spectral stability theory for onestep 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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