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12. 6. 2024.
Some Modifications of the Trapezoidal Rule
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