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An interpolation degenerate kernel method for eigenvalue problems of a class of non-compact operators

✍ Scribed by H. Majidian; E. Babolian

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
261 KB
Volume
23
Category
Article
ISSN
0893-9659

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✦ Synopsis

We consider the eigenvalue problem of a class of non-compact linear operators given as the sum of a multiplication and a kernel operator. A degenerate kernel method with piecewise constant interpolation with respect to the second variable is used to approximate isolated eigenvalues of finite type. The convergence of the method is proved, and it is shown that the error is of order O(h). The proposed method has been applied to some sample problems.

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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 subs