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Title: A technique for studying strong and weak local errors of splitting stochastic integrators
Authors: Álamo Zapatero, Alfonso
Sanz Serna, Jesús María
Issue Date: 2016
Publisher: Society for Industrial and Applied Mathematics
Citation: 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
Peer Review: SI
Sponsor: Ministerio de Economía, Industria y Competitividad (Project MTM2013-46553-C3-1-P).
Publisher Version:
Language: eng
Rights: info:eu-repo/semantics/openAccess
Appears in Collections:DEP51 - Artículos de revista

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