SLEIGN2

Algorithm 810: The SLEIGN2 Sturm-Liouville code. The SLEIGN2 code is based on the ideas and methods of the original SLEIGN code of 1979. The main purpose of the SLEIGN2 code is to compute eigenvalues and eigenfunctions of regular and singular self-adjoint Sturm-Liouville problems, with both separated and coupled boundary conditions, and to approximate the continuous spectrum in the singular case. The code uses some new algorithms, which we describe, and has a driver program that offers a user-friendly interface. In this paper the algorithms and their implementations are discussed, and the class of problems to which each algorithm applied is identified


References in zbMATH (referenced in 35 articles , 2 standard articles )

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  1. Gheorghiu, Călin-Ioan: Spectral collocation solutions to problems on unbounded domains (2018)
  2. Aceto, Lidia; Magherini, Cecilia; Weinmüller, Ewa B.: Matrix methods for radial Schrödinger eigenproblems defined on a semi-infinite domain (2015)
  3. Amodio, Pierluigi; Settanni, Giuseppina: Reprint of “Variable-step finite difference schemes for the solution of Sturm-Liouville problems” (2015)
  4. Amodio, Pierluigi; Settanni, Giuseppina: Variable-step finite difference schemes for the solution of Sturm-Liouville problems (2015)
  5. Yuan, S.; Ye, K.; Xiao, C.; Kennedy, D.; Williams, F.: Solution of regular second- and fourth-order Sturm-Liouville problems by exact dynamic stiffness method analogy (2014)
  6. Castillo-Pérez, Raúl; Kravchenko, Vladislav V.; Torba, Sergii M.: Spectral parameter power series for perturbed Bessel equations (2013)
  7. Makarov, V.L.; Dragunov, D.V.; Klimenko, Ya.V.: The FD-method for solving Sturm-Liouville problems with special singular differential operator (2013)
  8. Hao, Xiaoling; Sun, Jiong; Zettl, Anton: Canonical forms of self-adjoint boundary conditions for differential operators of order four (2012)
  9. Širca, Simon; Horvat, Martin: Computational methods for physicists. Compendium for students. Translated from the Slovenian. (2012)
  10. Katsevich, A.: Singular value decomposition for the truncated Hilbert transform. II. (2011)
  11. Hammerling, Robert; Koch, Othmar; Simon, Christa; Weinmüller, Ewa B.: Numerical solution of singular ODE eigenvalue problems in electronic structure computations (2010)
  12. Ledoux, Veerle; Van Daele, Marnix: Solution of Sturm-Liouville problems using modified Neumann schemes (2010)
  13. Ledoux, V.; Van Daele, M.; Vanden Berghe, Guido: Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics (2009)
  14. Lv, Haiyan; Shi, Yuming: Error estimate of eigenvalues of perturbed second-order discrete Sturm-Liouville problems (2009)
  15. Marlettta, Marco; Rozenblum, Grigori: A Laplace operator with boundary conditions singular at one point (2009)
  16. Fulton, Charles: Titchmarsh-Weyl $m$ -functions for second-order Sturm-Liouville problems with two singular endpoints (2008)
  17. Ishikawa, Hideaki: Numerical methods for the eigenvalue determination of second-order ordinary differential equations (2007)
  18. Williams, Fred W.; Watson, Andrew; Howson, W.Paul; Jones, Antonia J.: Exact solutions for Sturm-Liouville problems on trees via novel substitute systems and the Wittrick-Williams algorithm (2007)
  19. Yuan, Si; Ye, Kangsheng; Xiao, Cheng; Williams, F.W.; Kennedy, D.: Exact dynamic stiffness method for non-uniform Timoshenko beam vibrations and Bernoulli-Euler column buckling (2007)
  20. Gurski, K.F.; McFadden, G.B.; Miksis, M.J.: The effect of contact lines on the Rayleigh instability with anisotropic surface energy (2006)

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