Abstract
Some quadrature formulae using the derivatives of the integrand are discussed. As special cases are obtained generalizations of both the ordinary and the modified Romberg algorithms. In all cases the error terms are expressed in terms of Bernoulli polynomials and functions.
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Håvie, T. Some algorithms for numerical quadrature using the derivatives of the integrand in the integration interval. BIT 10, 277–294 (1970). https://doi.org/10.1007/BF01934198
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DOI: https://doi.org/10.1007/BF01934198