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A SPECIFIC STURM-LIOUVILLE DIFFERENTIAL EQUATION

ABSTRACT
Explicit solutions of the second order ordinary differential equation y′′(x)+(λ+12 sech2x)y(x)=0 and its eigenpairs are obtained by calculating complex residues. Eigenpairs (energey states and energy function), spectral function and eigenfunction expansions are also reported.
KEYWORDS
PAPER SUBMITTED: 2018-09-17
PAPER REVISED: 2018-10-08
PAPER ACCEPTED: 2018-10-27
PUBLISHED ONLINE: 2018-12-16
DOI REFERENCE: https://doi.org/10.2298/TSCI180917329T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 1, PAGES [S47 - S56]
REFERENCES
  1. Titchmarsh, E. C., Eigenfunction Expansions Associated with Second-Order Differential Equations Part I, Oxford University Press, Oxford, UK, 1962
  2. Kamke, E., Differentialgleichungen, Akademische Verlagsgesellschaft, Leipzig, Germany, 1943
  3. Tanriverdi, T., Boundary-Value Problems in ODE, Ph.D. thesis, University of Pittsburgh, Pittsburgh, USA, 2001
  4. Tanriverdi, T., McLeod, J. B., Generalization of the eigenvalues by contour integrals, Appl. Math. Comput., 189 (2007), 2, pp. 1765-1773
  5. Tanriverdi, T., McLeod, J. B., The Analysis of Contour Integrals, Abstr. Appl. Anal., 2008 (2008), pp. 1-12
  6. Tanriverdi, T., Contour integrals associated differential equations, Math. Comput. Modelling, 49(2009), (3-4), pp. 453-462
  7. Tanriverdi, T., Differential equations with contour integrals, Integral Transforms Spec. Funct., 20(2009), 2, pp. 119-125
  8. Everitt, W.N., A catalogue of Sturm-Liouville differential equations, Birkhauser Verlag, Basel, 2005, pp. 271-331
  9. Hahn, D. W., Ozisik, M. N., Heat Conduction, 3rd edition, Wiley, New York, USA, 2012
  10. Popović, M . E., There are two twin shadows, but Einstein is one, Thermal Science, (16) 2012, 1, pp. 1-6
  11. Wu, F., et al., Work output and efficiency of a reversible quantum otto cycle, Thermal Science, (14)2010, 4, pp. 879-886
  12. Krapez, J. C., Linear, trigonometric and hyperbolic profiles of thermal effusivity in the Liouville space and related quadrupoles: Simple analytical tools for modeling graded layers and multilayers, International Journal of Thermal Sciences, 136(2019), pp. 182-199

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence