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[MUG] Re: Numerical integration of functions with singularity
| [MUG] Re: Numerical integration of functions with singularity |
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Author: Robert Israel
Posted: 24/11/2000 00:42:17 GMT
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>> From: Robert Israel
Maple does numerical double integrals as iterated integrals. In the
process of doing this it will integrate f(x,y) for x from -10 to 10 for a
lot of different values of y. If it does this for y = 0, it will find
that int(f(x,0),x=-10..10) does not converge, and it won't be able to
do the double integral.
Maple does attempt singularity handling for (single) integrals, but that's
not usually going to work for double integrals. You might be able to help
it by expressing your function in polar coordinates around the
singularity. If the integrand has a singularity like 1/r at the origin,
this will disappear when you integrate in polar coordinates because of the
factor r in the area element r dr dtheta.
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
On Fri, 17 Nov 2000, Arvind Raman wrote:
> I am trying to integrate numerically a real valued function of x and y
> (too long to list) in a rectangular region say
>
> evalf( Int( Int(f(x,y),x=-10..10 ),y=-10..10) );
>
> The function is smooth and well behaved in the rectangle, however at (0,
> 0) a singularity occurs (function is unbounded).
> As I ran the above command, MAPLE returned with the following error
> message:
>
> Error, (in evalf/int) integrand has a pole in the interval
>
> My understanding was the MAPLE by default uses some signularity handling
>
> routines. Why can it not seem to integrate this problem which has the
> simplest of
> singularities (a pole)?
>
> thanks
>
> Arvind Raman
>
>
>
>
>
>
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