On the method of Chan and Lu for Abel's integral equation

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Abstract
For the method proposed recently by Chan and Lu (1981) for the inversion of Abel's integral equation, the authors show that (i) under a wide range of circumstances, it yields numerical schemes identical with those obtained from the direct discretisation of the standard inversion formulae; (ii) although it avoids the explicit numerical differentiation in the standard inversion formulae, it does not avoid the numerical difficulties inherent in the inversion; and (iii) it is still equivalent mathematically and numerically to a half-differentiation.