BIT Numerical Mathematics

, Volume 33, Issue 4, pp 654–669

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


  • Diego Bricio Hernandez
    • CIMAT
    • DMMMSA, Università di Padova
  • Renato Spigler
    • CIMAT
    • DMMMSA, Università di Padova
Part II Numerical Mathematics

DOI: 10.1007/BF01990541

Cite this article as:
Hernandez, D.B. & Spigler, R. BIT (1993) 33: 654. doi:10.1007/BF01990541


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)60H1034F0565L0793E15

Keywords and phrases

Numerical stabilityRunge-Kutta methodsimplicit methodsstochastic differential equationsstochastic stability

Copyright information

© the BIT Foundation 1993