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Stable strong order 1.0 schemes for solving stochastic ordinary differential equations

Alcock, Jamie & Burrage, Kevin (2012) Stable strong order 1.0 schemes for solving stochastic ordinary differential equations. BIT Numerical Mathematics, 52(3), pp. 539-557.

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Abstract

The Balanced method was introduced as a class of quasi-implicit methods, based upon the Euler-Maruyama scheme, for solving stiff stochastic differential equations. We extend the Balanced method to introduce a class of stable strong order 1. 0 numerical schemes for solving stochastic ordinary differential equations. We derive convergence results for this class of numerical schemes. We illustrate the asymptotic stability of this class of schemes is illustrated and is compared with contemporary schemes of strong order 1. 0. We present some evidence on parametric selection with respect to minimising the error convergence terms. Furthermore we provide a convergence result for general Balanced style schemes of higher orders.

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ID Code: 53878
Item Type: Journal Article
Keywords: Numerical methods, Stability, Stochastic differential equations
DOI: 10.1007/s10543-012-0372-6
ISSN: 1572-9125
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Springer Science + Business Media B.V
Deposited On: 28 Sep 2012 12:47
Last Modified: 13 Oct 2012 13:03

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