A Method to Approximate Solution of the First Kind Abel Integral Equation Using Navots Quadrature and Simpsons 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 weakly singular integrals. by using sidi's sin^m - transformation and modied 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 efficiency of the mentioned method.