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

de Boor, Carl; Swartz, Blair

doi:10.1090/S0025-5718-1981-0595038-4

Collocation approximation to eigenvalues of an ordinary differential equation: numerical illustrations
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by Carl de Boor and Blair Swartz PDF

Math. Comp. 36 (1981), 1-19 Request permission

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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Elementary Numerical Analysis

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