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http://dx.doi.org/10.14317/jami.2014.567

RICHARDSON EXTRAPOLATION OF ITERATED DISCRETE COLLOCATION METHOD FOR EIGENVALUE PROBLEM OF A TWO DIMENSIONAL COMPACT INTEGRAL OPERATOR  

Panigrahi, Bijaya Laxmi (Department of Mathematics, Sambalpur University)
Nelakanti, Gnaneshwar (Department of Mathematics, Indian Institute of Technology Kharagpur)
Publication Information
Journal of applied mathematics & informatics / v.32, no.5_6, 2014 , pp. 567-584 More about this Journal
Abstract
In this paper, we consider approximation of eigenelements of a two dimensional compact integral operator with a smooth kernel by discrete collocation and iterated discrete collocation methods. By choosing numerical quadrature appropriately, we obtain convergence rates for gap between the spectral subspaces, and also we obtain superconvergence rates for eigenvalues and iterated eigenvectors. We then apply Richardson extrapolation to obtain further improved error bounds for the eigenvalues. Numerical examples are presented to illustrate theoretical estimates.
Keywords
Eigenvalue problem; compact integral operator; Discrete collocation methods; Richardson extrapolation;
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