Legendre multi-projection methods for solving eigenvalue problems for a compact integral operator

• Autores: Bijaya Laxmi Panigrahi, Guangqing Long, Gnaneshwar Nelakanti
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 239, Nº 1, 2013, págs. 135-151
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.09.014
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• Resumen

  • In this paper, we consider the M-Galerkin and M-collocation methods for solving the eigenvalue problem for a compact integral operator with smooth kernels, using Legendre polynomial bases. We obtain error bounds for the eigenvalues and the gap between the spectral subspaces in both LegendreM-Galerkin and LegendreM-collocation methods. We also obtain superconvergence results for the eigenvalues and iterated eigenvectors in both L2 and infinity norm. We illustrate our results with numerical examples.