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Boundary Integral Equations with the Generalized Neumann Kernel for the Neumann Problem

Author(s): Mohamed M. S. Nasser

Journal: Matematika
ISSN 0127-8274

Volume: 23;
Issue: 2;
Start page: 83;
Date: 2007;
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Keywords: Neumann problem | Fredholm integral equation | Generalized Neumann kernel.

This paper presents a new method to solve the interior and the exterior Neumann problems in simply connected regions with smooth boundaries. The method is based on two uniquely solvable Fredholm integral equations of the second kind with the generalized Neumann kernel. Numerical examples reveal that the present method offers an effective numerical method for the Neumann problems when the boundaries are sufficiently smooth.
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