Some approximations of second order derivatives complex-valued functions

In this paper, we generalize the well known finite difference method to compute derivatives of real valued function to approximate of second order complex derivatives w(zz) and w((zz) over bar) for complex-valued function w. Exploring different combinations of terms, we derive several approximations to compute the second order derivatives of complex-valued function. Several second order of accuracy finite differences to calculate derivatives are proposed. Error analysis in test examples is carried out by using Matlab program.