Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation

Authors:
Mingzhu Liu;Wanrong Cao;Zhencheng Fan
Affiliations:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

The paper deals with convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation. It is proved that the semi-implicit Euler method is convergent with strong order p=½. The conditions under which the method is MS-stable and GMS-stable are determined and the numerical experiments are given.