TY - JOUR
T1 - Convergence and Stability of the Semi-Implicit Euler Method with Variable Stepsize for a Linear Stochastic Pantograph Differential Equation
AU - Y. Xiao, M. Song & M. Liu
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 214
EP - 225
PY - 2011
DA - 2011/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/683.html
KW - Stochastic pantograph differential equation, mean square stability, semi-implicit Euler method with variable stepsize.
AB - <p style="text-align: justify;">The paper deals with convergence and stability of the semi-implicit
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 $p = \frac{1}{2}$. The conditions
under which the method is mean square stability are determined and the
numerical experiments are given.</p>