Abstract
In this paper, a split-step θ algorithm is proposed for nonlinear stochastic variable delay differential equations. It is proved that the numerical solution obtained by the algorithm converges to the exact solution under the local Lipschitz condition. Moreover, it is shown that the numerical algorithm can maintain the mean square stability of the analytical solution for linear scalar equations. Finally, numerical experiments demonstrate the correctness of the theoretical algorithm.
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Correction Statement
This article has been republished with minor changes. These changes do not impact the academic content of the article.