New nite di erence formulas for numerical di erentiation
نویسندگان
چکیده
Conventional numerical di erentiation formulas based on interpolating polynomials, operators and lozenge diagrams can be simpli ed to one of the nite di erence approximations based on Taylor series, and closed-form expressions of these nite di erence formulas have already been presented. In this paper, we present new nite di erence 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 di erentiation of a function at a speci ed mesh point. c © 2000 Elsevier Science B.V. All rights reserved.
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