Superconvergence of Legendre projection methods for the eigenvalue problem of a compact integral operator |
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Authors: | Bijaya Laxmi Panigrahi Gnaneshwar Nelakanti |
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Institution: | Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India |
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Abstract: | In this paper, we consider the Galerkin and collocation methods for the eigenvalue problem of a compact integral operator with a smooth kernel using the Legendre polynomials of degree ≤n. We prove that the error bounds for eigenvalues are of the order O(n−2r) and the gap between the spectral subspaces are of the orders O(n−r) in L2-norm and O(n1/2−r) in the infinity norm, where r denotes the smoothness of the kernel. By iterating the eigenvectors we show that the iterated eigenvectors converge with the orders of convergence O(n−2r) in both L2-norm and infinity norm. We illustrate our results with numerical examples. |
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Keywords: | Eigenvalues Eigenvectors Legendre polynomials Compact operator Superconvergence rates Integral equations |
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