Study on split-step Rosenbrock type method for stiff stochastic differential systems

ABSTRACT

In this paper, we present a split-step Rosenbrock type method for stiff stochastic differential systems. The method is proved to be mean-square (MS) convergent with strong order $\frac{1}{2}$. For one- and two-dimensional Itô test equations with multiplicative noise, we analysis asymptotically MS stability and plot asymptotic MS stability regions. Numerical examples and simulations are given to illustrate the effectiveness of theoretical results.

KEYWORDS:

• Stiff stochastic differential system
• split-step Rosenbrock type method
• ODEs solver
• mean-square convergence
• asymptotically mean-square stability

2010 AMS SUBJECT CLASSIFICATIONS:

• 60H10
• 65C20
• 65L20

Acknowledgements

The authors are grateful to the editor and the anonymous reviewers for their careful reading, insightful comments and helpful suggestions which have led to improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the Research Council of Semnan University.