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oai:uvadoc.uva.es:10324/288592025-03-26T19:10:04Zcom_10324_1176com_10324_931com_10324_894col_10324_1359

Alamo Zapatero, Alfonso Sanz Serna, Jesús María 2018-03-01T12:36:44Z 2018-03-01T12:36:44Z 2016 SIAM J. Numer. Anal. 54-6 (2016), pp. 3239-3257 0036-1429 http://uvadoc.uva.es/handle/10324/28859 10.1137/16M1058765 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. eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 International A technique for studying strong and weak local errors of splitting stochastic integrators info:eu-repo/semantics/article