Some approximations of second order derivatives complex-valued functions

Abstract

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 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.