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Convergence and stability in mean square of the stochastic θ-methods for systems of NSDDEs under a coupled monotonicity condition

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  • Niu, Mengyao
  • Niu, Yuanling
  • Wei, Jiaxin

Abstract

Our research is devoted to investigating the convergence and stability in mean square of the stochastic θ-methods applied to neutral stochastic differential delay equations (NSDDEs) with super-linearly growing coefficients. Under a coupled monotonicity condition, we show that the numerical approximations of the stochastic θ-methods with θ∈[12,1] converge to the exact solution of NSDDEs strongly with order 12. Moreover, it is shown that the stochastic θ-methods are capable of preserving the stability of the exact solution of original equations for any given stepsize h>0. Finally, several numerical examples are presented to illustrate the theoretical findings.

Suggested Citation

  • Niu, Mengyao & Niu, Yuanling & Wei, Jiaxin, 2025. "Convergence and stability in mean square of the stochastic θ-methods for systems of NSDDEs under a coupled monotonicity condition," Applied Mathematics and Computation, Elsevier, vol. 498(C).
    • Handle: RePEc:eee:apmaco:v:498:y:2025:i:c:s0096300325001225
    DOI: 10.1016/j.amc.2025.129395
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    References listed on IDEAS

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    1. Zhou, Shaobo, 2015. "Exponential stability of numerical solution to neutral stochastic functional differential equation," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 441-461.
    2. Li, Xiuping & Cao, Wanrong, 2015. "On mean-square stability of two-step Maruyama methods for nonlinear neutral stochastic delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 373-381.
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