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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.

  • AMS Subject Headings

65C30, 65L20, 60H10

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-214, author = {}, 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 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 & M. Liu. (1970). 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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