Mathematics of Computation

Eigenvalues of periodic Sturm-Liouville problems by the Shannon-Whittaker sampling theorem

Author(s): Amin Boumenir.
Journal: Math. Comp. 68 (1999), 1057-1066.
MSC (1991): Primary 34L15, 42A15
Posted: February 10, 1999
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Abstract: We are concerned with the computation of eigenvalues of a periodic Sturm-Liouville problem using interpolation techniques in Paley-Wiener spaces. We shall approximate the Hill discriminant by sampling a few of its values and then find its zeroes which are the square roots of the eigenvalues. Computable error estimates are provided together with eigenvalue enclosures.

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Amin Boumenir
Affiliation: Department of Mathematics, College of Sciences, Sultan Qaboos University, P.O. Box 36, Alkhod 123, Muscat, Sultanate of Oman
Email: boumenir@squ.edu.om

DOI: 10.1090/S0025-5718-99-01053-4
PII: S 0025-5718(99)01053-4
Keywords: Periodic Sturm-Liouville problems, eigenvalue problem, interpolation, Shannon-Whittaker sampling theorem
Received by editor(s): June 9, 1997
Received by editor(s) in revised form: October 28, 1997
Posted: February 10, 1999
Copyright of article: Copyright 1999, American Mathematical Society

Amin Boumenir, A Rigorous Verification of a Numerically Computed Eigenvalue, Comput. Math. Appl. (7-8) 38 (1999), 39-41.

Amin Boumenir, The recovery of Analytic potentials, Inverse Problems (6) 15 (1999), 1405-1423.

Amin Boumenir, Higher approximation of eigenvalues by sampling, BIT (2) 40 (2000), 215-225.

Amin Boumenir, The sampling method for Sturm-Liouville problems with the eigenvalue parameter in the boundary condition, Numer.Funct.Anal.Optimiz (1-2) 21 (2000), 67-75.

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