Standard and Corrected Numerical Differentiation Formulae

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Communications in Advanced Mathematical Sciences
Volume:2 Issue:2
Standard and Corrected Numerical Differentiation Formulae

Standard and Corrected Numerical Differentiation Formulae

Pages : 135-153

View : 40 | Download : 10

Publication Date : 2019-06-27

Article Type : Research Paper

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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