The numerical differentiation of discrete functions using polynomial interpolation methods

摘要

A FORTRAN subroutine package, called DERMOD, has been written for calculating numerical approximations for the spatial derivatives of a function defined only on a discrete set of data points. The routines are designed to complement many existing codes for solving ordinary and partial differential equations and for the interpolation of tabular data. We describe some new numerical differentiation algorithms, discuss a mapping procedure for nonuniform grids, and explain the program methodology used in designing the software.