New formula 4IgSFD_L of Zhang finite difference for 1st-order derivative approximation with numerical experiment verification

In this paper, aiming at discretizing continuous-time systems, a new formula of the improved finite difference, Zhang finite difference (ZFD), termed 4-instant g-square finite difference of subtype L (4IgSFD_L) is proposed with g denoting the sampling gap. The derivation and the corresponding numerical experiments of this new formula are also presented. Based on Taylor series expansion, the finite difference approximations can obtain numerical differentiation with high efficacy and accuracy, and this new formula is different from existing formulas, because it uses one ahead instant, two back instants and the target instant alternatively to obtain the derivative at the target instant. Moreover, substantiated by numerical experimental results, the approximation error of 4IgSFD_L has a pattern of O(g
²
).