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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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To our knowledge, the only numerical methods for the equation (1.1) 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].