Volume 8, Issue 2
Convergence and Stability of the Semi-implicit Euler Method with Variable Stepsize for a Linear Stochastic Pantograph Differential Equation

Y. Xiao ,  M. Song and M. Liu

Int. J. Numer. Anal. Mod., 8 (2011), pp. 214-225

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  • Abstract

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.

  • History

Published online: 2011-08

  • AMS Subject Headings

65C30, 65L20, 60H10

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