An efficient numerical method for solving Abel integral equation

In this paper, a numerical method for solving Abel integral equation is presented. We first convert the integral equation to the algebraic equation. Then we find numerical inversion of Laplace transform by power series. At last the Padé approximants is effectively used to improve the convergence rate and accuracy of the computed series. The method is described and illustrated with numerical examples. The results reveal that the method is accurate and easy to implement.