Also called Radau Quadrature (Chandrasekhar 1960). A Gaussian Quadrature with Weighting Function
in which the endpoints of the interval are included in a total of Abscissas, giving free
abscissas. Abscissas are symmetrical about the origin, and the general Formula is
(1) |
(2) | |||
(3) |
(4) |
(5) |
3 | 0 | 1.33333 |
± 1 | 0.333333 | |
4 | ± 0.447214 | 0.833333 |
± 1 | 0.166667 | |
5 | 0 | 0.711111 |
± 0.654654 | 0.544444 | |
± 1 | 0.100000 | |
6 | ± 0.285232 | 0.554858 |
± 0.765055 | 0.378475 | |
± 1 | 0.0666667 |
The Abscissas and weights can be computed analytically for small .
3 | 0 | |
4 | ||
5 | 0 | |
See also Chebyshev Quadrature, Radau Quadrature
References
Abramowitz, M. and Stegun, C. A. (Eds.).
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, pp. 888-890, 1972.
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 465, 1987.
Chandrasekhar, S. Radiative Transfer. New York: Dover, pp. 63-64, 1960.
Hildebrand, F. B. Introduction to Numerical Analysis. New York: McGraw-Hill, pp. 343-345, 1956.
© 1996-9 Eric W. Weisstein