Underlying one-step methods and nonautonomous stability of general linear methods
Numerical Analysis
2017-09-08 v1
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. 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.
Cite
@article{arxiv.1709.02059,
title = {Underlying one-step methods and nonautonomous stability of general linear methods},
author = {Andrew J. Steyer and Erik S. Van Vleck},
journal= {arXiv preprint arXiv:1709.02059},
year = {2017}
}