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New finite difference formulas for numerical differentiation

I. R. Khan
R. Ohba
Journal / Anthology

Journal of Computational & Applied Mathematics
Year: 2000
Volume: 126
Issue: 1-2
Page range: 269-276

Conventional numerical differentiation formulas based on interpolating polynomials, operators and lozenge diagrams can be simplified to one of the finite difference approximations based on Taylor series, and closed-form expressions of these finite difference formulas have already been presented. In this paper, we present new finite difference formulas, which are more accurate than the available ones, especially for the oscillating functions having frequency components near the Nyquist frequency. Closed-form expressions of the new formulas are given for arbitrary order. A comparison of the previously available three types of approximations is given with the presented formulas. A computer program written in Mathematica, based on new formulas is given in the appendix for numerical differentiation of a function at a specified mesh point.

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Calculus

finite difference formulas, numerical differentiation, Taylor series, closed-form expressions