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Spectral corrections for Sturm-Liouville problems. (English) Zbl 0988.65057

The authors discuss the numerical integration of linear 1-D Sturm-Liouville problems in finite and infinite intervals. A shooting method is implemented both for the eigenvalues and the eigenfunctions. Newton iterations, with their typical advantages and risks, are used to calculate an approximation of an eigenvalue. A general formula for the global discretisation error is proposed together with an estimate for the eigenvalue error reported to work well for higher order eigenvalues. Solutions to a number of test examples support the findings.

MSC:

65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
34B24 Sturm-Liouville theory
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators
65L70 Error bounds for numerical methods for ordinary differential equations
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators

Software:

SLCPM12
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Full Text: DOI

References:

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