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Volume 4, Issue 6
Simulations of Two-Step Maruyama Methods for Nonlinear Stochastic Delay Differential Equations

Wanrong Cao & Zhongqiang Zhang

DOI: 10.4208/aamm.12-12S11

Adv. Appl. Math. Mech., 4 (2012), pp. 821-832.

Published online: 2012-12

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  • Abstract

In this paper, we investigate the numerical performance of a family of P-stable two-step Maruyama schemes in mean-square sense for stochastic differential equations with time delay proposed in [8, 10] for a certain class of nonlinear stochastic delay differential equations with multiplicative white noises. We also test the convergence of one of the schemes for a time-delayed Burgers' equation with an additive white noise. Numerical results show that this family of two-step Maruyama methods exhibit similar stability for nonlinear equations as that for linear equations.

  • Keywords

P-stability in mean-square sense, two-step Maruyama methods, nonlinear stochastic delay differential system, Burgers' equation.

  • AMS Subject Headings

65C20, 65C30, 65Q20

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{AAMM-4-821, author = {Cao , Wanrong and Zhang , Zhongqiang}, title = {Simulations of Two-Step Maruyama Methods for Nonlinear Stochastic Delay Differential Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {6}, pages = {821--832}, abstract = {

In this paper, we investigate the numerical performance of a family of P-stable two-step Maruyama schemes in mean-square sense for stochastic differential equations with time delay proposed in [8, 10] for a certain class of nonlinear stochastic delay differential equations with multiplicative white noises. We also test the convergence of one of the schemes for a time-delayed Burgers' equation with an additive white noise. Numerical results show that this family of two-step Maruyama methods exhibit similar stability for nonlinear equations as that for linear equations.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-12S11}, url = {http://global-sci.org/intro/article_detail/aamm/151.html} }
TY - JOUR T1 - Simulations of Two-Step Maruyama Methods for Nonlinear Stochastic Delay Differential Equations AU - Cao , Wanrong AU - Zhang , Zhongqiang JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 821 EP - 832 PY - 2012 DA - 2012/12 SN - 4 DO - http://doi.org/10.4208/aamm.12-12S11 UR - https://global-sci.org/intro/article_detail/aamm/151.html KW - P-stability in mean-square sense, two-step Maruyama methods, nonlinear stochastic delay differential system, Burgers' equation. AB -

In this paper, we investigate the numerical performance of a family of P-stable two-step Maruyama schemes in mean-square sense for stochastic differential equations with time delay proposed in [8, 10] for a certain class of nonlinear stochastic delay differential equations with multiplicative white noises. We also test the convergence of one of the schemes for a time-delayed Burgers' equation with an additive white noise. Numerical results show that this family of two-step Maruyama methods exhibit similar stability for nonlinear equations as that for linear equations.

Cao , Wanrong and Zhang , Zhongqiang. (2012). Simulations of Two-Step Maruyama Methods for Nonlinear Stochastic Delay Differential Equations. Advances in Applied Mathematics and Mechanics. 4 (6). 821-832. doi:10.4208/aamm.12-12S11
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