A Nystrom method for Fredholm integral equations with right hand sides having isolated singularities

Fredholm integral equations on the interval [−1, 1] with right-hand sides having isolated singularities are considered. The original equation is reduced to an equivalent system of Fredholm integral equations with smooth input functions. The Nyström method is applied to the system after a polynomial regularization. The convergence, stability and well conditioning of the method is proved in spaces of weighted continuous functions. The special case of the weakly singular and symmetric kernel is also investigated. Several numerical tests are included.