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We propose an efficient and flexible method for solving Abel integralequation of the first kind, frequently appearing in many fields ofastrophysics, physics, chemistry, and applied sciences. This equationrepresents an ill-posed problem, thus solving it requires some kind ofregularization. Our method is based on solving the equation on a so-calledcompact set of functions and/or using Tikhonov's regularization. A prioriconstraints on the unknown function, defining a compact set, are very loose andcan be set using simple physical considerations. Tikhonov's regularization onitself does not require any explicit a priori constraints on the unknownfunction and can be used independently of such constraints or in combinationwith them. Various target degrees of smoothness of the unknown function may beset, as required by the problem at hand. The advantage of the method, apartfrom its flexibility, is that it gives uniform convergence of the approximatesolution to the exact solution, as the errors of input data tend to zero. Themethod is illustrated on several simulated models with known solutions. Anexample of astrophysical application of the method is also given.

An efficient and flexible Abel-inversion method for noisy data