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Guaranteed Error Bounds for Eigenvalues of Singular Sturm-Liouville Problems

✍ Scribed by B.M. Brown; D.K.R. McCormack; M. Marletta

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
272 KB
Volume
213
Category
Article
ISSN
0025-584X

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✦ Synopsis

We develop a simple oscillation theory for singular Sturm -Liouville problems and combine it with recent asymptotic results, and with the AWA interval-arithmetic code for integration of initial value problems with guaranteed error bounds, to obtain eigenvalue approximations with guaranteed error bounds for a class of singular Sturm -Liouville problems. We believe that this is the first time that this has been achieved for singular eigenvalue problems.

πŸ“œ SIMILAR VOLUMES

On the Maximum and Minimum of Some Funct
On the Maximum and Minimum of Some Functionals for the Eigenvalue Problem of Sturm-Liouville Type
✍ H.H. Chern; C.L. Shen πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 461 KB

Let \(\lambda_{n}(q)\) be the \(n\)th eigenvalue of the Sturm-Liouville equation \(y^{\prime \prime}+(\lambda-q(x)) y=0\), \(y(-l / 2)=y(l / 2)=0\). With certain restrictions on the class of functions \(q\) we determine the shapes of the solutions of the extremal problems for the functionals \(\lamb