Publications

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

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

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.