A note on a family of quadrature formulas and some applications

• Autorzy: Bożek B. , Solak W. , Szydełko Z.
• Języki publikacji: EN

Abstrakty

EN

In this paper a construction of a one-parameter family of quadrature formulas is presented. This family contains the classical quadrature formulas: trapezoidal rule, mid-point 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.

Słowa kluczowe

EN

quadrature and cubature formulas; numerical integration

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2008
• Tom: Vol. 28, no. 2
• Strony: 109--121
• Opis fizyczny: Bibliogr. 5 poz., rys., wykr., tab.

Twórcy

autor

Bożek B.

autor

Solak W.

autor

Szydełko Z.

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-065 Cracow, Poland,

Bibliografia

• [1] K. Atkinson, W. Han, Theoretical Numerical Analysis, A Functional Analysis Framework, Springer-Verlag, New York, 2001.
• [2] E. Hairer, S.P. Nørsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems, Springer, New York, 1993.
• [3] D. Kincaid, W. Cheney, Numerical Analysis, Mathematics of Scientific Computing, 3rd ed., The University of Texas at Austin, Brooks/Cole-Thomson Learning, 2002.
• [4] E. Nyström, Über die praktische Auflösung von Integralgleichungen mit Anwendungen auf Randwertaufgaben, Acta Math., 54 (1930), 185-204.
• [5] A.H. Stroud, Approximate Calculation of Multiple Integrals, Prentice-Hall, Englewood Cliffs, New Jersey, 1971.