A Method to Approximate Solution of the First Kind Abel Integral Equation Using Navotʹʹs Quadrature and Simpsonʹʹs Rule

In this paper, we present a method for solving the first kind Abel integral equation. In this method, the first kind Abel integral equation is transformed to the second kind Volterra integral equation with a continuous kernel and a smooth deriving term expressed by weakly singular integrals. By using Sidiʹs sin^m - transformation and modified Navot-Simpsonʹs integration rule, an algorithm for solving this kind of integral equation is proposed, then the convergence of algorithm is derived. Some numerical results show the efficiency of the mentioned method.