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On a Shooting Algorithm for Sturm-Liouville Eigenvalue Problems with Periodic and Semi-periodic Boundary Conditions

✍ Scribed by Xingzhi Ji

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 266 KB
Volume: 111
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.1994.1045

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✦ Synopsis

This paper is concerned with the eigenvalues of Sturm-Liouville problems with periodic and semi-periodic boundary conditions to be approximated by a shooting algorithm. The proposed technique is based on the application of the Floquet theory. Convergence analysis and a general guideline to provide starting values for computed eigenvalues are presented. Some numerical results are atso reported. :c 1994 Ae:ademic Press, Inc.

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## Abstract Let us consider the boundary‐value problem equation image where __g__: ℝ → ℝ is a continuous and __T__ ‐periodic function with zero mean value, not identically zero, (__λ__, __a__) ∈ ℝ^2^ and $ \tilde h $ ∈ __C__ [0, __π__ ] with ∫^__π__^ ~0~ $ \tilde h $(__x__) sin __x dx__ = 0. If _