Singularities at end point in integration

[ashesh]

singularities at end point in integration...

Hi,

I Need to perform an integration with poles and zeros in the integrand. Please let me know if there a MATLAB routine/program that can handle the definite integral

sqrt((x-a)*(x-b)/((x-c)*(x-d)))

between the limits (c,d), (a,d), (a,b) or (b,c).

I have read about the routine in quadpack called "dqawse.f" which can perform "integration of functions having algebraico-logarithmic end point singularities".

I need a MATLAB equivalent program that can perform this type of integration. I have checked gausscc.m file (http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=2905&objectType=file) which does integration by Chebychev-Curtis quadrature, but that seems to be no good in handling singularities.

Hope someone can give some leads to solve the above problem.

Thanks in advance.
Ashesh

 

[fresh_42]

I would use WoframAlpha if the parameters are known. If not, I'm not aware of a general solution to it, except perhaps a Taylor expansion.

 

[Gigaz]

Here's a simple approach:
Approximate the function by a simpler function at the singularity, which you can integrate analytically.
Integrate the singularity. Then integrate all the rest with your favorite numerical method.