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Some new four-point quadrature formulas. (English) Zbl 1199.65073

Summary: We present a new family of four-point quadrature formulas of close type. These quadrature formulas can be considered as generalizations of Gauss, Newton, Simpson and Lobatto quadrature formulas for different classes of functions. The optimal quadrature formulas in the sense of minimal errors are obtained. An analysis of error inequalities for different classes of functions is also given.

MSC:

65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
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