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Zbl 1210.65014
Wang, Wenqiang; Chen, Yanping
Mean-square stability of semi-implicit Euler method for nonlinear neutral stochastic delay differential equations. (English)
[J] Appl. Numer. Math. 61, No. 5, 696-701 (2011). ISSN 0168-9274

Summary: There are few results on the numerical stability of nonlinear neutral stochastic delay differential equations (NSDDEs). The aim of this paper is to establish some new results on the numerical stability for nonlinear NSDDEs. It is proved that the semi-implicit Euler method is mean-square stable under suitable condition. The theoretical result is also confirmed by a numerical experiment.

MSC 2000:: *65C30 Stochastic differential and integral equations
60H10 Stochastic ordinary differential equations
34K50 Stochastic delay equations
34K28 Numerical approximation of solutions of FDE
34K40 Neutral equations
60H35 Computational methods for stochastic equations

Keywords: semi-implicit Euler method; mean-square stability; numerical stability; nonlinear neutral stochastic delay differential equations; numerical experiment

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