Finite difference weights

Finds finite difference (or interpolation) weights for an arbitrary set of nodes in one dimension.

Given a vector of nodes x, a point of interest xi, and a nonnegative order of derivative m, this function returns weights such that an inner product with the values f(x) returns an approximation to f^(m)(xi). Based on the recursive formula due to Fornberg (A Practical Guide to Pseudospectral Methods, Cambridge University Press).

Examples from the file:

% First derivative near a boundary
h = 0.4; x = h*(0:5)';
w = fdweights(x(2),x,1)
[ w'*exp(x) exp(x(2)) ]

% Interpolation
x = [0 0.25 1 1.5 2.5]';
w = fdweights(0.5,x,0)
[ w'*sin(x) sin(0.5) ]