RT info:eu-repo/semantics/article
T1 A technique for studying strong and weak local errors of splitting stochastic integrators
A1 Álamo Zapatero, Alfonso
A1 Sanz Serna, Jesús María
AB 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.
PB Society for Industrial and Applied Mathematics
SN 0036-1429
YR 2016
FD 2016
LK http://uvadoc.uva.es/handle/10324/28859
UL http://uvadoc.uva.es/handle/10324/28859
LA eng
NO SIAM J. Numer. Anal. 54-6 (2016), pp. 3239-3257
DS UVaDOC
RD 02-dic-2024