Por favor, use este identificador para citar o enlazar este ítem:http://uvadoc.uva.es/handle/10324/28859
A technique for studying strong and weak local errors of splitting stochastic integrators
Año del Documento
Society for Industrial and Applied Mathematics
SIAM J. Numer. Anal. 54-6 (2016), pp. 3239-3257
We present a technique, based on so-called word series, to write down in a systematic way expansions of the strong and weak local errors of splitting algorithms for the integration of Stratonovich stochastic differential equations. Those expansions immediately lead to the corresponding order conditions. Word series are similar to, but simpler than, the B-series used to analyze Runge--Kutta and other one-step integrators. The suggested approach makes it unnecessary to use the Baker--Campbell--Hausdorff formula. As an application, we compare two splitting algorithms recently considered by Leimkuhler and Matthews to integrate the Langevin equations. The word series method clearly bears out reasons for the advantages of one algorithm over the other.
Revisión por pares
Ministerio de Economía, Industria y Competitividad (Project MTM2013-46553-C3-1-P).
Version del Editor
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivatives 4.0 International