Delay-dependent exponential stability of the backward Euler method for nonlinear stochastic delay differential equations

Authors:
Xiaomei Qu;Chengming Huang
Affiliations:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China;School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China
Venue:
International Journal of Computer Mathematics
Year:
2012

Citing 0
Cited 2

Delay-dependent stability analysis of numerical methods for stochastic delay differential equations

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Mean square stability and dissipativity of two classes of theta-methods for systems of stochastic delay differential equations

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Abstract

Recently, several scholars discussed the question of under what conditions numerical solutions can reproduce exponential stability of exact solutions to stochastic delay differential equations, and some delay-independent stability criteria were obtained. This paper is concerned with delay-dependent stability of numerical solutions. Under a delay-dependent condition for the stability of the exact solution, it is proved that the backward Euler method is mean-square exponentially stable for all positive stepsizes. Numerical experiments are given to confirm the theoretical results.