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

 
Opuscula Mathematica

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.

Full text (pdf)

  • 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
  • Received: 2007-01-04.
  • Revised: 2007-11-07.
  • Accepted: 2007-11-11.
Opuscula Mathematica - cover

Cite this article as:
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

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.