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

Table 1

Calculated intervals of step-size for mean-square stability of the numerical schemes.

Numerical scheme	Case 1	Case 2
Split-step θ-Milstein method (𝜃=0.0)	(0.0000, 0.0500]	(0.0000, 0.1000]
Split-step θ-Milstein method (𝜃=0.2)	(0.0000, 0.0625]	(0.0000, 0.1250]
Split-step θ-Milstein method (𝜃=0.5)	(0.0000, 0.1000]	(0.0000, 0.2000]
Split-step θ-Milstein method (𝜃=0.8)	(0.0000, 0.0650)	(0.0000, 0.5000]
Split-step θ-Milstein method (𝜃=1.0)	(0.0000, 0.0500)	(0.0000, 0.3534)
Split-step 𝜃-method (𝜃=0.0)	(0.0000, 0.0500]	(0.0000, 0.1000]
Split-step 𝜃-method (𝜃=0.2)	(0.0000, 0.0625]	(0.0000, 0.1250]
Split-step 𝜃-method (𝜃=0.5)	(0.0000, 0.1000]	(0.0000, 0.2000]
Split-step 𝜃-method (𝜃=0.8)	(0.0000, 0.0689)	(0.0000, 0.5000]
Split-step 𝜃-method (𝜃=1.0)	(0.0000, 0.0540)	(0.0000, 0.5792)