A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

Burrage, Kevin, Burrage, Pamela, & Belward, John (1997) A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations. BIT Numerical Mathematics, 37(4), pp. 771-780.

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In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

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ID Code: 57938
Item Type: Journal Article
Refereed: Yes
Keywords: Runge-Kutta methods
DOI: 10.1007/BF02510351
ISSN: 0006-3835
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Stochastic Analysis and Modelling (010406)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 12 Mar 2013 00:14
Last Modified: 12 Apr 2013 00:49

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