Asymptotic mean-square stability of linear multi-step methods for SODEs |
| |
Authors: | Evelyn Buckwar Renate Winkler |
| |
Institution: | Institut für Mathematik, Humboldt-Universität zu Berlin, 10099 Berlin, Germany |
| |
Abstract: | In this article we present results of a linear stability analysis of stochastic linear multi-step methods for stochastic ordinary differential equations. As in deterministic numerical analysis we use a linear time-invariant test equation and study when the numerical approximation shares asymptotic properties in the mean-square sense of the exact solution of that test equation. Sufficient conditions for asymptotic mean-square stability of stochastic linear two-step-Maruyama methods are obtained with the aide of Lyapunov-type functionals. In particular we study the asymptotic mean-square stability of stochastic counterparts of two-step Adams-Bashforth- and Adams-Moulton-methods and the BDF method. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) |
| |
Keywords: | |
|
|