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Manuscript Title: Inversion of Abel's integral equation by a direct method.
Authors: L.S. Fan, W. Squire
Program title: ABEL
Catalogue identifier: ABSC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 10(1975)98
Programming language: Fortran.
Computer: IBM 360/75.
Operating system: HASP.
RAM: 17K words
Word size: 16
Keywords: Plasma physics, Spectroscopy, Abel integral equation, Product integration, Spline interpolation, Data interpretation.
Classification: 19.4.

Nature of problem:
Determination of the radial distribution of the emission coefficient from the measured intensity distribution when the source is thin and axially symmetrical.

Solution method:
Abel's integral equation is inverted by a direct procedure using product integration. A procedure using splines is used for interpolating the data, which need not be equally spaced, to the needed points and to interpolate the solution to the desired output points. The integration is stopped a few steps short of the center because of the singularity and the solution is extrapolated by the spline procedure.

Restrictions:
The dimensioning of internal arrays limits the number of data points and the number of steps in the integration to 300 points, also no provision is made for smoothing data.

Running time:
6 s for five sets of data (31 points each) and 60 steps in integration.