Abstract: | An approximation of function u(x) as a Taylor series expansion about a point x0 at M points xi, ~ i = 1,2,…,M is used where xi are arbitrary‐spaced. This approximation is a linear system for the derivatives u(k) with an arbitrary accuracy. An analytical expression for the inverse matrix A ?1 where A = [Aik] = (xi ? x0)k is found. A finite‐difference approximation of derivatives u(k) of a given function u(x) at point x0 is derived in terms of the values u(xi). © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 |