TY  - JOUR
ID  - Bożek2008
LB  - Bożek2008
AU  - Bożek, Bogusław
AU  - Solak, Wiesław
AU  - Szydełko, Zbigniew
TI  - A note on a family of quadrature formulas and some applications
ST  - A note on a family of quadrature formulas and some applications
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2008
VL  - 28
IS  - 2
SP  - 109
EP  - 121
DO  - http://dx.doi.org/10.7494/OpMath.2008.28.2.109
UR  - http://dx.doi.org/10.7494/OpMath.2008.28.2.109
AB  - 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.
KW  - quadrature and cubature formulas
KW  - numerical integration
SN  - 1232-9274
ER  -