From: "Dann Corbit" Subject: Re: Double Exponential Date: Fri, 1 Sep 2000 13:32:10 -0700 Newsgroups: sci.math.num-analysis Summary: [missing] "N&J" wrote in message news:8op366$206o$1@ulysses.noc.ntua.gr... > Hi all, > I recently read in a journal that there is a method for numerical > integration called "Double Exponential Integration" which can integrate > singular integrals. Actually Maple V uses this method if the variable change > fails. I have not been able to find any resources concerning this method , > Can anyone tell me where to find information about it on the web? It is a remarkably stable and useful method. It is good for oscillating functions and infinite intervals and all sorts of such things. You can find code for it here in Fortran and C: http://momonga.t.u-tokyo.ac.jp/~ooura/ See also: Davis and Rabinowitz, Methods of Numerical Integration, pp. 214 Di Marco G., Favati P., Lotti G. & Romani F., Asymptotic Behaviour of Automatic Quadrature, J. Complexity, 1994, 10, 296-340. M.Mori, Developments in the double exponential formula for numerical integration, Proceedings of the International Congress of Mathematicians, Kyoto 1990, 1991, Springer-Verlag, 1585-1594. H.Takahasi and M.Mori, Double exponential formulas for numerical integration, Pub. RIMS Kyoto Univ. 9, 1974, 721-741 T.Ooura and M.Mori, The Double exponential formula for oscillatory functions over the half infinite interval, Journal of Computational and Applied Mathematics 38, 1991, 353-360 M.Mori and T.Ooura, Double exponential formulas for Fourier type integrals with a divergent integrand, Contributions in Numerical Mathematics, ed. R.P.Agarwal, World Scientific Series in Applicable Analysis, 2, 1993, 301-308 H.Toda and H.Ono, Some remarks for efficient usage of the double exponential formulas(in Japanese), Kokyuroku, RIMS, Kyoto Univ. 339, 1978, 74-109. -- C-FAQ: http://www.eskimo.com/~scs/C-faq/top.html "The C-FAQ Book" ISBN 0-201-84519-9 C.A.P. Newsgroup http://www.dejanews.com/~c_a_p C.A.P. FAQ: ftp://38.168.214.175/pub/Chess%20Analysis%20Project%20FAQ.htm