منابع مشابه
A corrected quadrature formula and applications
A straightforward 3-point quadrature formula of closed type is derived that improves on Simpson’s rule. Just using the additional information of the integrand’s derivative at the two endpoints we show the error is sixth order in grid spacing. Various error bounds for the quadrature formula are obtained to quantify more precisely the errors. Applications in numerical integration are given. With ...
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Abstract—This paper deals with efficient quadrature formulas involving functions that are observed only at fixed sampling points. The approach that we develop is derived from efficient continuous quadrature formulas, such as Gauss-Legendre or Clenshaw-Curtis quadrature. We select nodes at sampling positions that are as close as possible to those of the associated classical quadrature and we upd...
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The basis of this paper is the quadrature formula where q = exp(2A), h being a chosen step length. This formula has been derived from the Trapezoidal Rule formula by F. Stenger. An explicit form of the error is given for the case where the integrand has a factor of the form (1 — x)a(\ + x)P, a,ß> -1. Application is made to the evaluation of Cauchy principal value integrals with endpoint singula...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1973
ISSN: 0021-9045
DOI: 10.1016/0021-9045(73)90110-x