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

N. Egidi and P. Maponi

Mathematics and Computers in Simulation (MATCOM), 2010, vol. 81, issue 3, 693-704

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 L2 integral kernel. Finally, a boundary value problem for the Laplace equation is considered as an example of the application of the proposed method.

Keywords: Fredholm integral equation; Iterative method; Sherman–Morrison formula (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2010:i:3:p:693-704

DOI: 10.1016/j.matcom.2010.03.006

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