Table of Contents
Advances in Numerical Analysis
Volume 2012, Article ID 349618, 21 pages
http://dx.doi.org/10.1155/2012/349618
Research Article

A Note on Fourth Order Method for Doubly Singular Boundary Value Problems

Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India

Received 31 May 2012; Accepted 5 September 2012

Academic Editor: Hassan Safouhi

Copyright © 2012 R. K. Pandey and G. K. Gupta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. E. Bobisud, “Existence of solutions for nonlinear singular boundary value problems,” Applicable Analysis, vol. 35, no. 1–4, pp. 43–57, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. L. H. Thomas, “The calculation of atomic fields,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 23, no. 5, pp. 542–548, 1927. View at Publisher · View at Google Scholar
  3. E. Fermi, “Un methodo statistico per la determinazione di alcune proprieta dell'atomo,” Atti dell'Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali, vol. 6, pp. 602–607, 1927. View at Google Scholar
  4. C. Y. Chan and Y. C. Hon, “A constructive solution for a generalized Thomas-Fermi theory of ionized atoms,” Quarterly of Applied Mathematics, vol. 45, no. 3, pp. 591–599, 1987. View at Google Scholar · View at Zentralblatt MATH
  5. L. E. Bobisud, D. O'Regan, and W. D. Royalty, “Singular boundary value problems,” Applicable Analysis, vol. 23, no. 3, pp. 233–243, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. L. E. Bobisud, D. O'Regan, and W. D. Royalty, “Solvability of some nonlinear boundary value problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 12, no. 9, pp. 855–869, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. E. Hille, “Some aspects of the Thomas-Fermi equation,” Journal d'Analyse Mathématique, vol. 23, no. 1, pp. 147–170, 1970. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. A. Granas, R. B. Guenther, and J. Lee, “Nonlinear boundary value problems for ordinary differential equations,” Dissertationes Mathematicae, vol. 244, p. 128, 1985. View at Google Scholar · View at Zentralblatt MATH
  9. D. R. Dunninger and J. C. Kurtz, “Existence of solutions for some nonlinear singular boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 115, no. 2, pp. 396–405, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. R. K. Pandey and A. K. Verma, “Existence-uniqueness results for a class of singular boundary value problems arising in physiology,” Nonlinear Analysis: Real World Applications, vol. 9, no. 1, pp. 40–52, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. R. K. Pandey and A. K. Verma, “A note on existence-uniqueness results for a class of doubly singular boundary value problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 3477–3487, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. R. K. Pandey and A. K. Verma, “On solvability of derivative dependent doubly singular boundary value problems,” Journal of Applied Mathematics and Computing, vol. 33, no. 1-2, pp. 489–511, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. Y. Zhang, “A note on the solvability of singular boundary value problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 26, no. 10, pp. 1605–1609, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. G. W. Reddien, “Projection methods and singular two point boundary value problems,” Numerische Mathematik, vol. 21, pp. 193–205, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. M. M. Chawla and C. P. Katti, “Finite difference methods and their convergence for a class of singular two-point boundary value problems,” Numerische Mathematik, vol. 39, no. 3, pp. 341–350, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. R. K. Pandey and A. K. Singh, “On the convergence of a finite difference method for a class of singular boundary value problems arising in physiology,” Journal of Computational and Applied Mathematics, vol. 166, no. 2, pp. 553–564, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. R. K. Pandey and A. K. Singh, “On the convergence of finite difference methods for weakly regular singular boundary value problems,” Journal of Computational and Applied Mathematics, vol. 205, no. 1, pp. 469–478, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. M. M. Chawla and C. P. Katti, “A uniform mesh finite difference method for a class of singular two-point boundary value problems,” SIAM Journal on Numerical Analysis, vol. 22, no. 3, pp. 561–565, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. M. M. Chawla, “A fourth-order finite difference method based on uniform mesh for singular two-point boundary-value problems,” Journal of Computational and Applied Mathematics, vol. 17, no. 3, pp. 359–364, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. M. M. Chawla, R. Subramanian, and H. L. Sathi, “A fourth-order spline method for singular two-point boundary value problems,” Journal of Computational and Applied Mathematics, vol. 21, no. 2, pp. 189–202, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. M. M. Chawla, R. Subramanian, and H. L. Sathi, “A fourth order method for a singular two-point boundary value problem,” BIT Numerical Mathematics, vol. 28, no. 1, pp. 88–97, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. R. K. Pandey and A. K. Singh, “On the convergence of fourth-order finite difference method for weakly regular singular boundary value problems,” International Journal of Computer Mathematics, vol. 81, no. 2, pp. 227–238, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. R. K. Pandey and A. K. Singh, “A new high-accuracy difference method for a class of weakly nonlinear singular boundary-value problems,” International Journal of Computer Mathematics, vol. 83, no. 11, pp. 809–817, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. R. K. Pandey and A. K. Singh, “On the convergence of a fourth-order method for a class of singular boundary value problems,” Journal of Computational and Applied Mathematics, vol. 224, no. 2, pp. 734–742, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, John Wiley & Sons, New York, NY, USA, 1962.