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Zbl 1063.33028
Volkmer, Hans
Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. (English)
[J] Constructive Approximation 20, No. 1, 39-54 (2004). ISSN 0176-4276; ISSN 1432-0940/e

The Rayleigh-Ritz method yields a decreasing sequence $\mu_r$ that approximates the desired eigenvalue $\lambda $ of Mathieu function or of spheroidal wave function. The method produces also a sequence of elementary functions $g$ that approximates the desired eigenfunction $f$ of the same functions. This paper provides answers to some questions about the rate of convergence $\mu _r\to \lambda $ and $g_r \to f$ as $r\to \infty $, to the error bounds for the maximum norm $\Vert g_r -f \Vert _\infty $ and to other convergence properties of the method. Errors are investigated by interesting numerical experimentations.
[Luigi Gatteschi (Torino)]

MSC 2000:: *33E10 Spheroidal wave functions, etc.
65L60 Finite numerical methods for ODE
65L70 Error bounds (numerical methods for ODE)

Keywords: Rayleigh-Ritz method; Mathieu equation; Spheroidal wave equation; tridiagonal matrix; error estimates.

Cited in: Zbl 1197.47046

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