Richardson Extrapolation of Iterated Discrete Galerkin Method for Eigenvalue Problem of a Two Dimensional Compact Integral Operator

Authors:
Bijaya Laxmi Panigrahi;Gnaneshwar Nelakanti
Affiliations:
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India 721302;Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India 721302
Venue:
Journal of Scientific Computing
Year:
2012

Citing 4
Cited 0

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SIAM Journal on Numerical Analysis
Richardson extrapolation of iterated discrete Galerkin solution for two-dimensional Fredholm integral equations

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A Fast Collocation Method for Eigen-Problems of Weakly Singular Integral Operators

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Abstract

We consider approximation of eigenelements of a two-dimensional compact integral operator with a smooth kernel by discrete Galerkin and iterated discrete Galerkin methods. By choosing numerical quadrature appropriately, we obtain superconvergence rates for eigenvalues and iterated eigenvectors, and for gap between the spectral subspaces. We propose an asymptotic error expansions of the iterated discrete Galerkin method and asymptotic error expansion of approximate eigenvalues. We then apply Richardson extrapolation to obtain improved error bounds for the eigenvalues. Numerical examples are presented to illustrate theoretical estimate.