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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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Volume 16, Issue 3


Approximating eigenvalues of discontinuous problems by sampling theorems

M. H. Annaby
  • *Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
  • Department of Mathematics and Physics, Qatar University, P.O. Box 2713 Doha, Qatar
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/ R. M. Asharabi
Published Online: 2008-11-24 | DOI: https://doi.org/10.1515/JNUM.2008.008


We use sampling techniques to compute eigenvalues of discontinuous second order boundary value problems. The eigenvalues are in general complex numbers and are not necessarily simple. Therefore error estimates for the truncation and amplitude errors on ℂ of the sampling expansion and its termwise derivative are used. Moreover the problem we consider has two parts throughout [–1,1] and is not in general self adjoint. The boundary and compatibility conditions are assumed to be regular in the sense of Birkhoff to guarantee the existence of eigenvalues.

Keywords:: sampling theory in Paley–Wiener spaces; truncation and amplitude errors; discontinuous eigenvalue problems; Birkhoff regularity

About the article

Received: 2008-01-30

Revised: 2008-05-05

Published Online: 2008-11-24

Published in Print: 2008-11-01

Citation Information: Journal of Numerical Mathematics, Volume 16, Issue 3, Pages 163–183, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/JNUM.2008.008.

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