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 Nyström 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.

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

FERMO, LUISA
2009

Abstract

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 Nyström 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.
Fredholm integral equations; Nyström method; Applied Mathematics; Computational Mathematics; Numerical Analysis
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/122779
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