Re: Integrable singularity
beliavsky_at_aol.com
Date: 01/29/05
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Date: 29 Jan 2005 14:33:07 -0800
Madhusudan Singh wrote:
> beliavsky@aol.com wrote:
>
> > Madhusudan Singh wrote:
> >> I wish to numerically integrate a real function with an
integrable
> >> singularity.
> >>
> >> What are the recommended methods for accomplishing the above ?
> >
> > Numerical Recipes in Fortran 77, section 4.4 has a discussion and
code
> > for this. You can download the pdf file from
> > http://www.library.cornell.edu/nr/ . One can use an "open"
quadrature
> > formula, which does not evaluate the function at the endpoints of
the
> > integration region. Alternatively, a variable transformation can
often
> > remove the singularity.
>
> Thanks for the info.
>
> The function I need to work on needs to be integrated in [0,\infty)
and has
> a singularity at a finite x0 \in [0,\infty).
Assuming x0 is known, one can separately compute the integrals on
(0,x0) and (x0,+inf). The "classic" Fortran (77) quadrature library is
quadpack at http://www.netlib.org/quadpack/ , and I think that library
has codes to handle integrals with endpoint singularities and with
semi-infinite domains.
Some quadpack codes have been translated to F90-style codes by Alan
Miller -- search "integration" at http://users.bigpond.net.au/amiller/
.
Many Fortran codes for numerical quadrature by Alan Genz, a researcher
in the subject, are at
http://www.math.wsu.edu/faculty/genz/software/software.html . John
Burkhardt has some quadrature codes at
http://www.csit.fsu.edu/~burkardt/f_src/f_src.html .
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