On Sinc-Based Method in Computing Eigenvalues of Boundary-Value Problems

We aim in this paper to give a complete treatment of the error analysis of the use of the sine method in computing eigenvalues of second order Birkhoff-regular eigenvalue problems. For this task we study truncation and amplitude errors on C associated with cardinal series representation of band-limi...

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Bibliographic Details
Published in:SIAM journal on numerical analysis Vol. 46; no. 2; pp. 671 - 690
Main Authors: Annaby, M. H., Asharabi, R. M.
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2008
Subjects:
Applied mathematics
Approximation
Boundary conditions
Eigenvalues
Error analysis
Fourier transforms
Mathematical functions
Methods
Series convergence
Sine function
Truncation
Truncation errors
ISSN:0036-1429, 1095-7170
Online Access:Get full text
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Summary:We aim in this paper to give a complete treatment of the error analysis of the use of the sine method in computing eigenvalues of second order Birkhoff-regular eigenvalue problems. For this task we study truncation and amplitude errors on C associated with cardinal series representation of band-limited functions as well as those of their derivatives. These results, which seem to be considered for the first time, give us the possibility to establish the error analysis when the eigenvalues are not real or not algebraically simple.
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ISSN:0036-1429
1095-7170
DOI:10.1137/060664653