[SciPy-User] numerical integration with square root like singularity

Daniel Platz mail.to.daniel.platz@googlemail....
Thu Nov 24 08:16:22 CST 2011


Hi,

I am stuck with a problem in scipy. I want to numerically integrate a
function with a square root like singularity at one end of the
integration interval. The integral has the form

\int_{0}^{1} f(x) * x / sqrt(1-x**2) dx

or alternatively

\int_{0}^{A} f(x) / sqrt(A-x) dx.

Can the quad function in scipy deal with this kind of singularity. I
tried to use the points argument of the quad function but I still get
warning messages and do not know how much I can trust the results.

Alternatively, I was wondering if I can implement a Chebyshev–Gauss
quadrature myself to lift the singularity? Or is there a way to do
this elegantly using scipy?

I would be very glad about a short answer.

Best regards,

Daniel Platz


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