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

Qian Guo, Wenwen Xie and Taketomo Mitsui

Abstract and Applied Analysis, 2013, vol. 2013, 1-12

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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:169214

DOI: 10.1155/2013/169214

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