Newton-Cotes formulas


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Newton-Cotes formulas

[′nüt·ən ′kōts ‚fȯr·myə·ləz]
(mathematics)
Approximation formulas for the integral of a function along a small interval in terms of the values of the function and its derivatives.
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1) have been constructed in [6, 7], where Direct Quadrature (DQ) methods based on Newton-Cotes formulas have been proposed.
It is known that Gaussian formulas ensure a higher order of accuracy and have better stability properties than Newton-Cotes formulas [2].
2, we have compared our results with those obtained by the only other numerical approach we know, that is, DQ methods based on Newton-Cotes formulas (in particular the trapezoidal and Simpson 3/8 formulas) [7]: the errors of the two families of methods are very similar, in spite of the error of approximation due to the interpolation technique used for the Gaussian formulas.