Radau quadrature formula
From Encyclopedia of Mathematics
A quadrature formula of highest algebraic accuracy for the interval 
and with weight 
, with one fixed node, namely an end point of the interval, say 
. The Radau quadrature formula has the form
 |
The nodes 
are the roots of the Jacobi polynomial 
(the Jacobi polynomials form an orthogonal system on 
with weight 
), and 
. The coefficients 
are positive. The algebraic degree of accuracy is 
. There exist tables of the nodes and coefficients for the Radau quadrature formula, see, for example, [2].
The formula was found by R. Radau [1].
References
| [1] | R. Radau, "Etude sur les formules d'approximation qui servent à calculer la valeur numérique d'une intégrale définie" J. Math. Pures et Appl. , 6 (1880) pp. 283–336 |
| [2] | V.I. Krylov, "Approximate calculation of integrals" , Macmillan (1962) (Translated from Russian) |
| [3] | A.M. Stroud, D. Secrest, "Gaussian quadrature formulas" , Prentice-Hall (1966) |
How to Cite This Entry:
Radau quadrature formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Radau_quadrature_formula&oldid=34104
Radau quadrature formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Radau_quadrature_formula&oldid=34104
This article was adapted from an original article by I.P. Mysovskikh (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article