Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

Burrage, K. and Tian, T. (2002) Predictor-corrector methods of Runge-Kutta type for stochastic differential equations. SIAM: Journal on Numerical Analysis, 40(4), pp. 1516-1537. (doi: 10.1137/S0036142900372677)

Abstract

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge--Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Tian, Dr Tianhai
• Authors: Burrage, K., and Tian, T.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: SIAM: Journal on Numerical Analysis
• ISSN: 0036-1429
• ISSN (Online): 1095-7170