Convergence and stability of the semi-implicit Euler method with variable stepsize for a linear stochastic Pantograph differential equation
Y. Xiao 1, M. Song 1, M. Liu 11 Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, P.R. China.
Received by the editors August 8, 2008 and, in revised form, July 20, 2010.
The paper deals with convergence and stability of the semiimplicit Euler method with variable stepsize for a linear stochastic pantograph differential equation(SPDE). It is proved that the semi-implicit Euler method with variable stepsize is convergent with strong order p = 1/2. The conditions under which the method is mean square stability are determined and the numerical experiments are given.AMS subject classifications: 65C30, 65L20, 60H10
Key words: Stochastic pantograph differential equation, mean square stability, semi-implicit Euler method with variable stepsize.
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