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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 & M. Liu

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

Published online: 2011-08

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  • Abstract

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.

  • Keywords

Stochastic pantograph differential equation, mean square stability, semi-implicit Euler method with variable stepsize.

  • AMS Subject Headings

65C30, 65L20, 60H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-214, author = {Y. Xiao, M. Song and M. Liu}, title = {Convergence and Stability of the Semi-Implicit Euler Method with Variable Stepsize for a Linear Stochastic Pantograph Differential Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {2}, pages = {214--225}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/683.html} }
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 -

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.

Y. Xiao, M. Song and M. Liu. (2011). Convergence and Stability of the Semi-Implicit Euler Method with Variable Stepsize for a Linear Stochastic Pantograph Differential Equation. International Journal of Numerical Analysis and Modeling. 8 (2). 214-225. doi:
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