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Collocation approximation to eigenvalues of an ordinary differential equation: numerical illustrations


Authors: Carl de Boor and Blair Swartz
Journal: Math. Comp. 36 (1981), 1-19
MSC: Primary 65L15
DOI: https://doi.org/10.1090/S0025-5718-1981-0595038-4
MathSciNet review: 595038
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Abstract: We display the numerical results associated with the collocation of three eigenvalue problems using from one to four Gauss points per partition interval in order to document the sharpness of the error bounds we have previously obtained. The ordinary differential operators involved are real with constant coefficients; two of the problems have an eigenvalue whose ascent exceeds one. We propose an explanation for the observed manner in which a set of simple approximate eigenvalues can approach a single multiple eigenvalue.


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DOI: https://doi.org/10.1090/S0025-5718-1981-0595038-4
Keywords: Eigenvalues, ordinary differential equation, collocation, piecewise polynomial, ascent of an eigenvalue, asymptotics of eigenvalue approximations
Article copyright: © Copyright 1981 American Mathematical Society