High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

Burrage, Kevin & Burrage, Pamela (1996) High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations. Applied Numerical Mathematics, 22(1-3), pp. 81-101.

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The pioneering work of Runge and Kutta a hundred years ago has ultimately led to suites of sophisticated numerical methods suitable for solving complex systems of deterministic ordinary differential equations. However, in many modelling situations, the appropriate representation is a stochastic differential equation and here numerical methods are much less sophisticated. In this paper a very general class of stochastic Runge-Kutta methods is presented and much more efficient classes of explicit methods than previous extant methods are constructed. In particular, a method of strong order 2 with a deterministic component based on the classical Runge-Kutta method is constructed and some numerical results are presented to demonstrate the efficacy of this approach.

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104 citations in Scopus
95 citations in Web of Science®
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ID Code: 57771
Item Type: Journal Article
Refereed: Yes
Keywords: Runge-Kutta Methods, Stochastic differential equations
DOI: 10.1016/S0168-9274(96)00027-X
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: 04 Mar 2013 23:05
Last Modified: 12 Apr 2013 00:53

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