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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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 |
|---|---|
| Publication: | International Journal of Computer Mathematics |
| Publisher: | Taylor and Francis Group |
| 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 Interdisciplinary 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.ac.in/id/eprint/44271 |
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