  Zhang Neural Networks rely on convergent 1-step ahead finite difference
formulas of which very few are known. Those which are known have been
constructed in ad-hoc ways and suffer from low truncation error orders. This
paper develops a constructive method to find convergent look-ahead finite
difference schemes of higher truncation error orders. The method consists of
seeding the free variables of a linear system comprised of Taylor expansion
coefficients followed by a minimization algorithm for the maximal magnitude
root of the formula's characteristic polynomial. This helps us find new
convergent 1-step ahead finite difference formulas of any truncation error
order. Once a polynomial has been found with roots inside the complex unit
circle and no repeated roots on it, the associated look-ahead ZNN
discretization formula is convergent and can be used for solving any
discretized ZNN based model. Our method recreates and validates the few known
convergent formulas, all of which have truncation error orders at most 4. It
also creates new convergent 1-step ahead difference formulas with truncation
error orders 5 through 8.
