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

J. Steyer, Andrew; S. Van Vleck, Erik

doi:10.3934/dcdsb.2018108

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

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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:

J. Steyer, Andrew ^[1]; S. Van Vleck, Erik ^[2]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Univ. of Kansas, Lawrence, KS (United States)

Publication Date:: Sat Sep 01 00:00:00 EDT 2018

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.

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                    J. Steyer, Andrew, & S. Van Vleck, Erik. Underlying one-step methods and nonautonomous stability of general linear methods.  United States.  https://doi.org/10.3934/dcdsb.2018108

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                    J. Steyer, Andrew, and S. Van Vleck, Erik. Sat .  
"Underlying one-step methods and nonautonomous stability of general linear methods".  United States.  https://doi.org/10.3934/dcdsb.2018108.  https://www.osti.gov/servlets/purl/1467393.

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@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         = {Sat Sep 01 00:00:00 EDT 2018},

  month        = {Sat Sep 01 00:00:00 EDT 2018}

}

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