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Five-stage Milstein methods for SDEs

Singh, Samar and Raha, Soumyendu (2012) Five-stage Milstein methods for SDEs. In: International Journal of Computer Mathematics, 89 (6). pp. 760-779.

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/0020716...

Abstract

In this paper, we consider the problem of computing numerical solutions for Ito stochastic differential equations (SDEs). The five-stage Milstein (FSM) methods are constructed for solving SDEs driven by an m-dimensional Wiener process. The FSM methods are fully explicit methods. It is proved that the FSM methods are convergent with strong order 1 for SDEs driven by an m-dimensional Wiener process. The analysis of stability (with multidimensional Wiener process) shows that the mean-square stable regions of the FSM methods are unbounded. The analysis of stability shows that the mean-square stable regions of the methods proposed in this paper are larger than the Milstein method and three-stage Milstein methods.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Taylor and Francis Group.
Keywords: stochastic differential equation;explicit method;mean convergence;mean-square convergence;stability
Department/Centre: Division of Information Sciences > Supercomputer Education & Research Centre
Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 13 Apr 2012 09:08
Last Modified: 13 Apr 2012 09:08
URI: http://eprints.iisc.ernet.in/id/eprint/44271

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