A Nystrom method for a class of Fredholm integral equations of the third kind on unbounded domains

The author proposes a numerical procedure in order to approximate the solution of a class of Fredholm integral equations of the third kind on unbounded domains. The given equation is transformed in a Fredholm integral equation of the second kind. Hence. according to the integration interval, the equation is regularized by means of a suitable one-to-one map or is transformed in a system of two Fredholm integral equations that are subsequently regularized. In both cases a Nystrom method is applied, the convergence and the stability of which are proved in spaces of weighted continuous functions. Error estimates and numerical tests are also included. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.