In order to approximate functions dened on (0, +∞), the authors consider suitable Lagrange polynomials and show their convergence in weighted L p -spaces.
In this paper the authors propose numerical methods to approximate the solutions of systems of second kind Fredholm integral equations. They prove that such methods are stable and convergent. Error estimates in weighted $L^p$ norm, $1\leq p\leq +∞$, are given and some numerical tests are shown
The authors consider the interior Dirichlet problem for Laplace's equation on planar domains with corners. In order to approximate the solution of the corresponding double layer boundary integral equation, they propose a numerical method of Nyström type, based on a Lobatto quadrature rule. The convergence and stability of the method are proved and some numerical tests are included.
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