Numerical methods for Fredholm integral equations based on Padua points

The numerical solution of two-dimensional Fredholm integral equations on the square by Nyström and collocation methods based on the Padua points is investigated. The convergence, stability and well conditioning of the methods are proved in suitable subspaces of continuous functions of Sobolev type. Some numerical examples illustrate the efficiency of the methods. A comparison with the tensorial approximation methods, of Nyström and collocation type, based on Legendre zeros, is given.