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Integration over a circle
Posted:
Jul 15, 1996 11:27 AM
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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 higher-order methods.
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