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Eigenvalue problem of a weakly singular compact integral operator by discrete legendre projection methods
, K. Kant, G. Nelakanti
Published in Wilmington Scientific Publisher
Volume: 11
Issue: 4
Pages: 2090 - 2101
In this article, the discrete version of Legendre projection and iterated Legendre projection methods are considered to find the approximate eigenfunctions (eigenvalues and eigenvectors) of a weakly singular compact integral operator. Making use of a sufficiently accurate numerical quadrature rule, we establish the error bounds of the approximated eigenvalues and eigenvectors by discrete Legendre projection and iterated discrete Legendre projection methods in both L2 and uniform norm. In particular, we obtain the optimal convergence rates O(n −m) for the eigenfunctions in iterated discrete Legendre projection method in L2 and uniform norms, where n is the highest degree of the Legendre polynomial employed in the approximation and m is the smoothness of the eigenvectors. Numerical examples are presented to illustrate the theoretical results. © 2021, Wilmington Scientific Publisher. All rights reserved.
About the journal
JournalJournal of Applied Analysis and Computation
PublisherWilmington Scientific Publisher