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Zbl 1059.65006
Liu, Mingzhu; Cao, Wanrong; Fan, Zhencheng
Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation. (English)
[J] J. Comput. Appl. Math. 170, No. 2, 255-268 (2004). ISSN 0377-0427

The authors prove conditions under which the semi-implicit Euler method has strong order of convergence 1/2 for scalar, linear stochastic differential delay equations. They also investigate mean square stability in terms of the stepsize of the method and the problem parameters. Numerical results illustrate some of the theory.
[Kevin Burrage (Brisbane)]

MSC 2000:: *65C30 Stochastic differential and integral equations
60H10 Stochastic ordinary differential equations
34F05 ODE with randomness
65L06 Multistep, Runge-Kutta, and extrapolation methods
65L20 Stability of numerical methods for ODE
60H35 Computational methods for stochastic equations

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

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