Implicit stochastic Runge-Kutta methods for stochastic differential equations

Burrage, K. and Tian, T. (2004) Implicit stochastic Runge-Kutta methods for stochastic differential equations. Bit Numerical Mathematics, 44 1: 21-39. doi:10.1023/B:BITN.0000025089.50729.0f


Author Burrage, K.
Tian, T.
Title Implicit stochastic Runge-Kutta methods for stochastic differential equations
Journal name Bit Numerical Mathematics   Check publisher's open access policy
ISSN 0006-3835
Publication date 2004-03-01
Sub-type Article (original research)
DOI 10.1023/B:BITN.0000025089.50729.0f
Volume 44
Issue 1
Start page 21
End page 39
Total pages 19
Editor A. Ruhe
Place of publication Netherlands
Publisher Kluwer Academic Publishers
Language eng
Abstract In this paper we construct implicit stochastic Runge-Kutta (SRK) methods for solving stochastic differential equations of Stratonovich type. Instead of using the increment of a Wiener process, modified random variables are used. We give convergence conditions of the SRK methods with these modified random variables. In particular, the truncated random variable is used. We present a two-stage stiffly accurate diagonal implicit SRK (SADISRK2) method with strong order 1.0 which has better numerical behaviour than extant methods. We also construct a five-stage diagonal implicit SRK method and a six-stage stiffly accurate diagonal implicit SRK method with strong order 1.5. The mean-square and asymptotic stability properties of the trapezoidal method and the SADISRK2 method are analysed and compared with an explicit method and a semi-implicit method. Numerical results are reported for confirming convergence properties and for comparing the numerical behaviour of these methods.
Keyword Stochastic Differential Equations
Runge-kutta Methods
Stiffly Accurate
Numerical Stability
Computer Science, Software Engineering
Mathematics, Applied
Stability
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 14:06:18 EST