Superconvergence of Legendre projection methods for the eigenvalue problem of a compact integral operator

✍ Scribed by Bijaya Laxmi Panigrahi; Gnaneshwar Nelakanti

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 277 KB
• Volume: 235
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2010.10.038

✦ Synopsis

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 L 2 -norm and O(n 1/2-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 L 2 -norm and infinity norm. We illustrate our results with numerical examples.