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.
Original language | English |
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Pages (from-to) | 539-557 |
Number of pages | 19 |
Journal | BIT Numerical Mathematics |
Volume | 52 |
Issue number | 3 |
DOIs | |
Publication status | Published - Sept 2012 |
Keywords
- Numerical methods
- Stability
- Stochastic differential equations
ASJC Scopus subject areas
- Software
- Computer Networks and Communications
- Computational Mathematics
- Applied Mathematics