Two-stage stochastic Runge-Kutta methods for stochastic differential equations

Tian, T. and Burrage, K. (2002) Two-stage stochastic Runge-Kutta methods for stochastic differential equations. BIT Numerical Mathematics, 42(3), pp. 625-643. (doi: 10.1023/A:1021963316988)

Abstract

In this paper we discuss two-stage diagonally implicit stochastic Runge-Kutta methods with strong order 1.0 for strong solutions of Stratonovich stochastic differential equations. Five stochastic Runge-Kutta methods are presented in this paper. They are an explicit method with a large MS-stability region, a semi-implicit method with minimum principal error coefficients, a semi-implicit method with a large MS-stability region, an implicit method with minimum principal error coefficients and another implicit method. We also consider composite stochastic Runge-Kutta methods which are the combination of semi-implicit Runge-Kutta methods and implicit Runge-Kutta methods. Two composite methods are presented in this paper. Numerical results are reported to compare the convergence properties and stability properties of these stochastic Runge-Kutta methods.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Tian, Dr Tianhai
• Authors: Tian, T., and Burrage, K.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: BIT Numerical Mathematics
• ISSN: 0006-3835
• ISSN (Online): 1572-9125
• Published Online: 03 November 2004