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Journal of Numerical Mathematics

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

Managing Editor: Olshanskii, Maxim

Editorial Board Member: 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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1569-3953
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Volume 16, Issue 3 (Jan 2008)

Issues

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
  • Other articles by this author:
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/ R. M. Asharabi
Published Online: 2008-11-24 | DOI: https://doi.org/10.1515/JNUM.2008.008

Abstract

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, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/JNUM.2008.008.

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A. H. Bhrawy, M. M. Tharwat, and A. Al-Fhaid
Abstract and Applied Analysis, 2012, Volume 2012, Page 1
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M. M. Tharwat, A. H. Bhrawy, and A. Yildirim
International Journal of Computer Mathematics, 2012, Volume 89, Number 15, Page 2061
[4]
M.H. Annaby and R.M. Asharabi
Journal of Approximation Theory, 2011, Volume 163, Number 3, Page 336
[5]
Mahmoud H. Annaby and Rashad M. Asharabi
Numerical Algorithms, 2012, Volume 60, Number 3, Page 355
[6]
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Journal of the Korean Mathematical Society, 2010, Volume 47, Number 6, Page 1299

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