Some Modifications of the Trapezoidal Rule - Udovičić, Zlatko (Sarajevo Journal of Mathematics, 2024)
By using the quadratic interpolating spline a new class of the quadrature rules was obtained. Those formulas are modifications of the well known trapezoidal rule. The basic characteristic of those formulas is a free parameter. With appropriate choice of that parameter, accuracy of the trapezoidal rule can be improved up to $O(h^4).$ Besides this, by using this nonstandard techniques some well known quadrature rules were also obtained. 2000 Mathematics Subject Classification. 65D32, 65D07