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Title: Numerical solution and spectrum of boundary-domain integral equation for the Neumann BVP with variable coefficient
Authors: Mikhailov, SE
Mohamed, NA
Keywords: Boundary-domain integral equations;Numerical solution;Iterative methods;Spectrum;Eigen-values
Issue Date: 2012
Publisher: Taylor & Francis
Citation: International Journal of Computer Mathematics, 89(11): 1488 - 1503, Apr 2012
Abstract: In this paper, a numerical implementation of a direct united boundary-domain integral equation (BDIE) related to the Neumann boundary value problem for a scalar elliptic partial differential equation with a variable coefficient is discussed. The BDIE is reduced to a uniquely solvable one by adding an appropriate perturbation operator. The mesh-based discretization of the BDIEs with quadrilateral domain elements leads to a system of linear algebraic equations (discretized BDIE). Then, the system is solved by LU decomposition and Neumann iterations. Convergence of the iterative method is discussed in relation to the distribution of eigenvalues of the corresponding discrete operators calculated numerically.
Description: This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 Taylor & Francis.
ISSN: 0020-7160
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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