A Method to Approximate Solution of the First Kind Abel Integral Equation Using Navot's Quadrature and Simpson's Rule

In this paper, we present a method for solving the rst kind Abel integral equation. In thismethod, the rst kind Abel integral equation is transformed to the second kind Volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. By using Sidi's sinm - transformation and modied Navot-Simpson'sintegration rule, an algorithm for solving this kind of integral equation is proposed, thenthe convergence of algorithm is derived. Some numerical results show the eciency of thementioned method.