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

Journal Article · 01 September 2018 · Discrete & Continuous Dynamical Systems - B

DOI: https://doi.org/10.3934/dcdsb.2018108 · OSTI ID:1467393

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

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

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.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
• Grant/Contract Number: AC04-94AL85000
• OSTI ID: 1467393
• Report Number(s): SAND--2018-3998J; 662444
• Journal Information: Discrete & Continuous Dynamical Systems - B, Journal Name: Discrete & Continuous Dynamical Systems - B Journal Issue: 7 Vol. 23; ISSN 1553-524X
• Country of Publication: United States
• Language: English