Numerical methods for Fredholm integral equations with singular right-hand sides

Abstract

Fredholm integral equations with the right-hand side having singularities at the endpoints are considered. The singularities are moved into the kernel that is subsequently regularized by a suitable one-to-one map. The Nystrom method is applied to the regularized equation. 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.