Nyström methods for bivariate Fredholm integral equations on unbounded domains

Abstract

In this paper we propose a numerical procedure in order to approximate the solution of two-dimensional Fredholm integral equations on unbounded domains like strips, half-planes or the whole real plane. We consider global methods of Nyström types, which are based on the zeros of suitable orthogonal polynomials. One of the main interesting aspects of our procedures regards the “quality” of the involved functions, since we can successfully manage functions which are singular on the finite boundaries and can have an exponential growth on the infinite boundaries of the domains. Moreover the errors of the methods are comparable with the error of best polynomial approximation in the weighted spaces of functions that we go to treat. The convergence and the stability of the methods and the well conditioning of the final linear systems are proved and some numerical tests, which confirm the theoretical estimates, are given.