Mean-square stability of second-order Runge-Kutta methods for multi-dimensional linear stochastic differential systems

Authors:
A. Rathinasamy;K. Balachandran
Affiliations:
Department of Mathematics, PSG Polytechnic College, Coimbatore 641 004, India;Department of Mathematics, Bharathiar University, Coimbatore 641 046, India
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 6
Cited 5

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Mean-square stability of second-order Runge-Kutta methods for stochastic differential equations

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Abstract

In this paper, the mean-square stability of second-order Runge-Kutta schemes for multi-dimensional linear stochastic differential systems is studied. Motivated by the work of Tocino [Mean-square stability of second-order Runge-Kutta methods for stochastic differential equations, J. Comput. Appl. Math. 175 (2005) 355-367] and Saito and Mitsui [Mean-square stability of numerical schemes for stochastic differential systems, in: International Conference on SCIentific Computation and Differential Equations, July 29-August 3 2001, Vancouver, British Columbia, Canada] we investigate the mean-square stability of second-order Runge-Kutta schemes for multi-dimensional linear stochastic differential systems with one multiplicative noise. Stability criteria are established and numerical examples that confirm the theoretical results are also presented.