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Título
A technique for studying strong and weak local errors of splitting stochastic integrators
Año del Documento
2016
Editorial
Society for Industrial and Applied Mathematics
Documento Fuente
SIAM J. Numer. Anal. 54-6 (2016), pp. 3239-3257
Abstract
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.
ISSN
0036-1429
Revisión por pares
SI
Patrocinador
Ministerio de Economía, Industria y Competitividad (Project MTM2013-46553-C3-1-P).
Version del Editor
Idioma
eng
Derechos
openAccess
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