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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. (English) Zbl 1063.33028
The Rayleigh-Ritz method yields a decreasing sequence μ r that approximates the desired eigenvalue λ 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 μ r λ and g r f as r, to the error bounds for the maximum norm g r -f and to other convergence properties of the method. Errors are investigated by interesting numerical experimentations.

MSC:
33E10Lamé, Mathieu, and spheroidal wave functions
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65L70Error bounds (numerical methods for ODE)
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