Projection Methods and Condition Numbers in Uniform Norm for Fredholm and Cauchy Singular Integral Equations

Abstract

In this paper the authors propose a numerical method for the approximate solution of some classes of Fredholm and Cauchy integral equations including the "discrete collocation" and "collocation" methods.

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

“…In [6] in order to approximate the solution of Eq. 1.1 (if it exists) the following numerical procedure was proposed.…”

“…There exists some numerical procedure that works also in the proposed case (see again [6]), but the convergence could be very slow.…”

“…The case when the right-hand side and the kernel are smooth functions was extensively investigated and there exists a wide literature about efficient numerical methods based on the polynomial approximation of the solution and on the Nyström methods (see for instance [1] and the bibliography therein and more recently [6]). …”

Numerical treatment of second kind Fredholm integral equations systems on bounded intervals

“…To this end, we look for a linear system whose solution allow us to compute f * m . We are going to study (3) in the spaces C v × C v and L p u × L p u , with v and u suitable Jacobi weights.…”

“…In this paper, extending an idea in [3,5], we propose a projection method and an equivalent Nyström-type method in different weighted L p spaces, 1 p + ∞. We show that such procedures are stable and convergent.…”