General 3-point quadrature formulas of Euler type (CROSBI ID 186977)
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Podaci o odgovornosti
Franjić, Iva ; Pečarić, Josip ; Perić, Ivan
engleski
General 3-point quadrature formulas of Euler type
General 3-point quadrature formulas for the approximate evaluation of an integral of a function f over [0, 1], through the values f(x), f(1/2), f(1-x), f'(0) and f'(1), are derived via the extended Euler formula. Such quadratures are sometimes called "corrected" or "quadratures with end corrections" and they have a higher accuracy than the adjoint classical formulas, which only include the values f(x), f(1/2), f(1-x). The Gauss 3-point, corrected Simpson, corrected dual Simpson, corrected Maclaurin and corrected Gauss 2-point formulas are recaptured as special cases. Finally, sharp estimates of error are given for this type of quadrature formula.
general 3-point quadrature formulas; corrected quadrature formulas; sharp estimates of error; Bernoulli polynomials; extended Euler formula
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