Convergence and Stability of the Split‐Step θ‐Milstein Method for Stochastic Delay Hopfield Neural Networks

Qian Guo, Wenwen Xie and Taketomo Mitsui

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: A new splitting method designed for the numerical solutions of stochastic delay Hopfield neural networks is introduced and analysed. Under Lipschitz and linear growth conditions, this split‐step θ‐Milstein method is proved to have a strong convergence of order 1 in mean‐square sense, which is higher than that of existing split‐step θ‐method. Further, mean‐square stability of the proposed method is investigated. Numerical experiments and comparisons with existing methods illustrate the computational efficiency of our method.

Date: 2013
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https://doi.org/10.1155/2013/169214

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:169214

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