Derivation of eigenrelations for the Sturm-Liouville boundary value problems with interior singularities
Author:
Thomas M. Acho
Journal:
Quart. Appl. Math. 65 (2007), 375-383
MSC (2000):
Primary 54B24, 34L20; Secondary 34E20, 33C15, 34E05
DOI:
https://doi.org/10.1090/S0033-569X-07-01048-7
Published electronically:
April 19, 2007
MathSciNet review:
2330563
Full-text PDF Free Access
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Abstract: Asymptotic solutions for the Sturm-Liouville boundary value problem with interior singularities were obtained using asymptotic forms of the Whittaker functions for higher order modes and the Titchmarsh-Weyl $m$-function for low order modes. However, these split interval techniques do not readily provide the eigenrelations for low order modes. For the first time, with minimal constraints, the eigenvalues for the Sturm-Liouville eigenproblem are obtained when the Titchmarsh-Weyl $m$-function technique is employed.
References
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References
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- Boyd J.P., Complex Co-ordinate Methods for Hydrodynamic Instabilities and Sturm-Liouville Eigenproblems with an Interior Singularity, Journal of Computational Physics, Vol. 54, No. 3, (1985) 454-471 MR 782992 (86g:65148)
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Additional Information
Thomas M. Acho
Affiliation:
Department of Mathematics and Applied Mathematics, University of the Free State, P.O. Box 339 Bloemfontein 9300, Republic of South Africa
Email:
achotm.blms@mail.uovs.ac.za
Keywords:
Asymptotic approximation,
interior singularities,
turning points,
Whittaker functions,
Titchmarsh-Weyl $m$-function,
direct sum method,
double pole,
split interval,
eigenfunction solutions,
eigenvalue relations,
high order modes,
low order modes.
Received by editor(s):
June 13, 2006
Received by editor(s) in revised form:
September 22, 2006
Published electronically:
April 19, 2007
Article copyright:
© Copyright 2007
Brown University
The copyright for this article reverts to public domain 28 years after publication.
