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

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.