Convergence and stability of implicit runge-kutta methods for systems with multiplicative noise
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A class ofimplicit Runge-Kutta schemes for stochastic differential equations affected bymultiplicative Gaussian white noise is shown to be optimal with respect to global order of convergence in quadratic mean. A test equation is proposed in order to investigate the stability of discretization methods for systems of this kind. Herestability is intended in a truly probabilistic sense, as opposed to the recently introduced extension of A-stability to the stochastic context, given for systems with additive noise. Stability regions for the optimal class are also given.
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- Convergence and stability of implicit runge-kutta methods for systems with multiplicative noise
BIT Numerical Mathematics
Volume 33, Issue 4 , pp 654-669
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- Kluwer Academic Publishers
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- 65L20 (primary)
- Numerical stability
- Runge-Kutta methods
- implicit methods
- stochastic differential equations
- stochastic stability
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