A Nyström 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 algebraic singularities and with a kernel that can have algebraic singularities at the end points are considered. The original equation is reduced to an equivalent system of Fredholm integral equations with smooth input functions. The Nystrom 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 a weakly singular and symmetric kernel is also investigated. Several numerical tests are included.
scientific article; zbMATH DE number 5617998
scientific article