Implicit Stochastic Runge–Kutta Methods for Stochastic Differential Equations |
| |
Authors: | Kevin Burrage Tianhai Tian |
| |
Institution: | (1) Department of Mathematics, University of Queensland, Brisbane, 4072, Australia |
| |
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.
This revised version was published online in July 2006 with corrections to the Cover Date. |
| |
Keywords: | stochastic differential equations Runge– Kutta methods stiffly accurate numerical stability |
本文献已被 SpringerLink 等数据库收录! |