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The Improved Stability Analysis of Numerical Method for Stochastic Delay Differential Equations

Author

Listed:
  • Yu Zhang

    (School of Economics, Harbin University of Commerce, Harbin 150028, China)

  • Enying Zhang

    (School of Economics, Harbin University of Commerce, Harbin 150028, China)

  • Longsuo Li

    (School of Management, Harbin Institute of Technology, Harbin 150001, China)

Abstract

In this paper, the improved split-step θ method, named the split-step composite θ method, is proposed to study the mean-square stability for stochastic differential equations with a fixed time delay. Under the global Lipschitz and linear growth conditions, it is proved that the split-step composite θ method with θ ≥ 0.5 shows mean-square stability. An approach to improving numerical stability is illustrated by choices of parameters of this method. Some numerical examples are presented to show the accordance between the theoretical and numerical results.

Suggested Citation

  • Yu Zhang & Enying Zhang & Longsuo Li, 2022. "The Improved Stability Analysis of Numerical Method for Stochastic Delay Differential Equations," Mathematics, MDPI, vol. 10(18), pages 1-7, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3366-:d:916540
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    References listed on IDEAS

    as
    1. Liu, Linna & Mo, Haoyi & Deng, Feiqi, 2019. "Split-step theta method for stochastic delay integro-differential equations with mean square exponential stability," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 320-328.
    2. Zhao, Guihua & Song, Minghui & Yang, Zhanwen, 2015. "Mean-square stability of analytic solution and Euler–Maruyama method for impulsive stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 527-538.
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