Standard and Corrected Numerical Differentiation Formulae

Year 2019, , 135 - 153, 27.06.2019

François Dubeau

https://doi.org/10.33434/cams.512796

Abstract

Standard numerical differentiation rules that might be established by the method of undetermined coefficients are revisited. Best truncation error bounds are established by a direct method and by the method of integration by parts "backwards". A new method to increase the order of the truncation error using a primitive is presented. This approach leads to corrected numerical differentiation rules. Differentiation formulae and numerical tests are presented.

Keywords

Absolutely continuous function, Method of undetermined coefficients, Numerical differentiation rules, Peano kernel, Taylor's expansion

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