Opuscula Mathematica
Opuscula Math. 28, no. 2 (2008), 109-121

A note on a family of quadrature formulas and some applications

Bogusław Bożek
Wiesław Solak
Zbigniew Szydełko
Abstract. In this paper a construction of a one-parameter family of quadrature formulas is presented. This family contains the classical quadrature formulas: trapezoidal rule, midpoint rule and two-point Gauss rule. One can prove that for any continuous function there exists a parameter for which the value of quadrature formula is equal to the integral. Some applications of this family to the construction of cubature formulas, numerical solution of ordinary differential equations and integral equations are presented.
Keywords: quadrature and cubature formulas, numerical integration.
Mathematics Subject Classification: 65D30, 65D32, 65L05, 65L06, 65R20.
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About the authors ▼
Bogusław Bożek
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-065 Cracow, Poland
Wiesław Solak
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-065 Cracow, Poland
Zbigniew Szydełko
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-065 Cracow, Poland
About the article ▼
Received: 2007-01-04.
Revised: 2007-11-07.
Accepted: 2007-11-11.
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Bogusław Bożek, Wiesław Solak, Zbigniew Szydełko, A note on a family of quadrature formulas and some applications, Opuscula Math. 28, no. 2 (2008), 109-121, http://dx.doi.org/10.7494/OpMath.2008.28.2.109.
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