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Radau quadrature formula

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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
This article was adapted from an original article by I.P. Mysovskikh (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article