BIT Numerical Mathematics

, Volume 51, Issue 3, pp 529–553 | Cite as

B-series analysis of iterated Taylor methods

Open Access


For stochastic implicit Taylor methods that use an iterative scheme to compute their numerical solution, stochastic B-series and corresponding growth functions are constructed. From these, convergence results based on the order of the underlying Taylor method, the choice of the iteration method, the predictor, and the number of iterations, for Itô and Stratonovich SDEs, and for weak as well as strong convergence are derived. As special case, also the application of Taylor methods to ODEs is considered. The theory is supported by numerical experiments.


Stochastic Taylor method Stochastic differential equation Iterative scheme Order Newton’s method Weak approximation Strong approximation Growth function Stochastic B-series 

Mathematics Subject Classification (2000)

65C30 60H35 65C20 68U20 


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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

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