The use of Sherman-Morrison formula in the solution of Fredholm integral equation of second kind

Authors:
N. Egidi;P. Maponi
Affiliations:
Universití di Camerino, Dipartimento di Matematica e Informatica, Camerino (MC) 62032, Italy;Universití di Camerino, Dipartimento di Matematica e Informatica, Camerino (MC) 62032, Italy
Venue:
Mathematics and Computers in Simulation
Year:
2010

Citing 3
Cited 0

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Abstract

We consider a constructive method for the solution of Fredholm integral equations of second kind. This method is based on a simple generalization of the well-known Sherman-Morrison formula to the infinite dimensional case. In particular, this method constructs a sequence of functions, that converges to the exact solution of the integral equation under consideration. A formal proof of this convergence result is provided for the case of Fredholm integral equations with L^2 integral kernel. Finally, a boundary value problem for the Laplace equation is considered as an example of the application of the proposed method.