Euler-precision general-form of Zhang et al discretization (ZeaD) formulas, derivation, and numerical experiments

In this paper, we propose and focus on a novel general-form of two-step Zhang et al discretization (ZeaD) formulas with truncation error proportional to the sampling gap of a certain system. Besides, the proposed general-form is applied to discretizing continuous-time Zhang neural network (CTZNN) with square precision in order to give a suitable discretization solution of future minimization. Specifically, to begin with, the stability and accuracy of the proposed general-form of the two-step ZeaD formulas are ensured by strict proof. Furthermore, its stability and accuracy are verified via approximation experiments. Last but not least, we present the discrete-time Zhang neural network (DTZNN) model by using our general-form of the two-step ZeaD formulas to discretize the CTZNN model, and inspect the stability and accuracy of our DTZNN models also through discretization experiments.