New ZFD (Zhang finite difference) formula 4IgSFD_L for time-varying reciprocal and inverse computation

Time-varying reciprocal and inverse computation are considered as fundamental problems in scientific and engineering fields, which are more complicated than static computation. Continuous-time Zhang dynamics (CTZD) model is a powerful method for such complicated situations. To obtain a discrete-time Zhang dynamics (DTZD) model, a new formula of 4-instant g-square finite difference (4IgSFD_L) is proposed in this paper. Note that the formula has a truncation error of O(g
²
), where g denotes the sampling gap. With the aid of the formula 4IgSFD_L, the 4IgSFD_L-type DTZD model is obtained. The 4IgSFD_L-type DTZD model has a high calculative precision with truncation error of O(g
³
). Through numerical experiments, the convergence and stability of 4IgSFD_L-type DTZD model are illustrated via time-varying reciprocal and inverse computation.