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Integration over a circle
Posted:
Jul 15, 1996 11:27 AM


I am interested in numericaly integrating a function over the surface of a circle (x^2+y^2<1). As a constraint, the function is not analytic, and evaluating it is relatively expensive in terms of time. I don't know how accurately the integration will need to be done  this is one of the points of interest. Fortunately it has no singularities and should be relatively smooth (and is always positive, if this helps). I have got as far as the 22 point scheme in Abromowitz and Stegun (in 25.4.61), but I don't know how to extend this formultation.
Since a circle is a simple shape, I suspect that better weighting schemes are available. I would appreciate any suggestions about where to go for higherorder methods.



