fdce

Finite difference coefficients estimator

Python implementation of the algorithm presented in:

Fornberg, B. (1988). Generation of finite difference formulas on arbitrarily spaced grids. Mathematics of computation, 51(184), 699-706.

This algorithm can estimate the coefficients of the finite difference formula used to estimate any derivative of an unidimensional function at a point x_0 given a grid of points (mostly neighbors of x_0). The accuracy level is determined by the number of grid points used in each estimation.

Highlights

• Grid points do not have to be equally spaced.
• x_0 does not have to be one of the grid points.
• As a result of 2., the algorithm can also be used to interpolate a function at a point x_0, by using the coefficients of the derivative of order zero.
• In a single M order derivative approximation the coefficients needed to estimate the derivative at any order from zero to M are calculated.