engleski

On corrected Euler-Simpson's 3/8 formulae

The aim of this paper is to derive corrected Euler-Simpson's 3/8 formulae, i.e. closed type quadrature formulae where the integral is approximated not only with the values of the function in points a, (2a+b)/3, (a+2b)/3 and b, but also with values of the first derivative at boundary points of the interval. These formulae will have a higher degree of exactness than the adjoint original formulae. Using the derived formulae, a number of inequalities for various classes of functions are obtained.

closed type quadrature formulae; corrected Simpson's 3/8 formulae; Bernoulli polynomials; functions of bounded variation; Lipschitzian functions

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