The composite Euler method for solving stiff stochastic differential equations

Burrage, K. and Tian, T. (2001) The composite Euler method for solving stiff stochastic differential equations. Journal of Computational and Applied Mathematics, 131(1-2), pp. 407-426. (doi: 10.1016/S0377-0427(00)00259-4)

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Abstract

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method.

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:Journal of Computational and Applied Mathematics
ISSN:0377-0427
Published Online:29 May 2001

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