Waveform relaxation method for stochastic differential equations with constant delay

Authors:
Zhencheng Fan
Affiliations:
Department of Mathematics, Minjiang University, Fuzhou 350108, China
Venue:
Applied Numerical Mathematics
Year:
2011

Citing 12
Cited 1

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Convergence analysis of waveform relaxation methods for neutral differential-functional systems

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On exponential mean-square stability of two-step Maruyama methods for stochastic delay differential equations

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Abstract

This paper extends the waveform relaxation method to stochastic differential equations with constant delay terms, gives sufficient conditions for the mean square convergence of the method. A lot of attention is paid to the rate of convergence of the method. The conditions of the superlinear convergence for a special case, which bases on the special splitting functions, are given. The theory is applied to a one-dimensional model problem and checked against results obtained by numerical experiments.