Hilbert transforms and Lagrange interpolation
Journal of Approximation Theory
A fast algorithm for particle simulations
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
A Collocation Method for the Generalized Airfoil Equation for an Airfoil with a Flap
SIAM Journal on Numerical Analysis
High order methods for weakly singular integral equations with nonsmooth input functions
Mathematics of Computation
Fast Collocation Methods for Second Kind Integral Equations
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Hybrid collocation methods for Fredholm integral equations with weakly singular kernels
Applied Numerical Mathematics
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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 Nyström 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.