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

Mengyao Niu, Yuanling Niu and Jiaxin Wei

Applied Mathematics and Computation, 2025, vol. 498, issue C

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.

Keywords: Neutral stochastic delay differential equations; Stochastic θ-methods; Convergence in mean square; Stability in mean square; Monotonicity condition (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:498:y:2025:i:c:s0096300325001225

DOI: 10.1016/j.amc.2025.129395

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