From: "Dann Corbit" <dcorbit@solutionsiq.com>
Subject: Re: Double Exponential
Date: Fri, 1 Sep 2000 13:32:10 -0700
Newsgroups: sci.math.num-analysis
Summary: [missing]

"N&J" <nikogian@hotmail.com> 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.

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