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

Burrage, K, Burrage, PM and Belward, JA (1997) A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations. BIT Numerical Mathematics, 37 4: 771-780.


Author Burrage, K
Burrage, PM
Belward, JA
Title A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations
Journal name BIT Numerical Mathematics
Publication date 1997
Sub-type Article
DOI 10.1007/BF02510351
Volume number 37
Issue number 4
ISSN 0006-3835; 1572-9125
Start page 771
End page 780
Total pages 10
Place of publication The Netherlands
Publisher Springer
Language eng
Subject 010302 Numerical Solution of Differential and Integral Equations
Formatted abstract 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 ans-stage SRK contains Stratonovich integrals up to orderp then the strong order of the SRK cannot exceed min{(p+1)/2, (s−1)/2},p≥2,s≥3 or 1 ifp=1.
Keyword Stochastic ordinary differential equation
Runge-Kutta methods
strong order
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article
Collection: Institute for Molecular Bioscience - Publications
 
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Created: Mon, 19 Jul 2010, 14:16:44 EST by Laura McTaggart on behalf of Institute for Molecular Bioscience