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Mean-square stability of semi-implicit Euler method for nonlinear neutral stochastic delay differential equations. (English) Zbl 1210.65014
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:
65C30Stochastic differential and integral equations
60H10Stochastic ordinary differential equations
34K50Stochastic functional-differential equations
34K28Numerical approximation of solutions of functional-differential equations
34K40Neutral functional-differential equations
60H35Computational methods for stochastic equations
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