Part II Numerical Mathematics

BIT Numerical Mathematics

, Volume 33, Issue 4, pp 654-669

First online:

Convergence and stability of implicit runge-kutta methods for systems with multiplicative noise

  • Diego Bricio HernandezAffiliated withCIMATDMMMSA, Università di Padova
  • , Renato SpiglerAffiliated withCIMATDMMMSA, Università di Padova

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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.

1980 AMS Subject Classification

65L20 (primary) 60H10 34F05 65L07 93E15

Keywords and phrases

Numerical stability Runge-Kutta methods implicit methods stochastic differential equations stochastic stability