Table of Contents
ISRN Computational Mathematics
Volume 2013 (2013), Article ID 262863, 11 pages
http://dx.doi.org/10.1155/2013/262863
Research Article

Solving a Class of Singular Two-Point Boundary Value Problems Using New Modified Decomposition Method

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

Received 10 November 2012; Accepted 5 January 2013

Academic Editors: T. Allahviranloo, L. S. Heath, E. Weber, and J. G. Zhou

Copyright © 2013 Randhir Singh and Jitendra Kumar. 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. 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 Scopus
  2. M. Kumar, “A fourth-order finite difference method for a class of singular two-point boundary value problems,” Applied Mathematics and Computation, vol. 133, no. 2-3, pp. 539–545, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. M. Inc and D. J. Evans, “The decomposition method for solving of a class of singular two-point boundary value problems,” International Journal of Computer Mathematics, vol. 80, no. 7, pp. 869–882, 2003. View at Publisher · View at Google Scholar · View at Scopus
  4. Z. Cen, “Numerical study for a class of singular two-point boundary value problems using Green's functions,” Applied Mathematics and Computation, vol. 183, no. 1, pp. 10–16, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Kumar and T. Aziz, “A uniform mesh finite difference method for a class of singular two-point boundary value problems,” Applied Mathematics and Computation, vol. 180, no. 1, pp. 173–177, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. S. H. Lin, “Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics,” Journal of Theoretical Biology, vol. 60, no. 2, pp. 449–457, 1976. View at Google Scholar · View at Scopus
  7. B. F. Gray, “The distribution of heat sources in the human head—theoretical consideration,” Journal of Theoretical Biology, vol. 82, no. 3, pp. 473–476, 1980. View at Google Scholar · View at Scopus
  8. G. Adomian, “Solution of the Thomas-Fermi equation,” Applied Mathematics Letters, vol. 11, no. 3, pp. 131–133, 1998. View at Publisher · View at Google Scholar · View at Scopus
  9. P. Jamet, “On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems,” Numerische Mathematik, vol. 14, no. 4, pp. 355–378, 1970. View at Publisher · View at Google Scholar · View at Scopus
  10. T. Aziz and M. Kumar, “A fourth-order finite-difference method based on non-uniform mesh for a class of singular two-point boundary value problems,” Journal of Computational and Applied Mathematics, vol. 136, no. 1-2, pp. 337–342, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Kumar, “A new finite difference method for a class of singular two-point boundary value problems,” Applied Mathematics and Computation, vol. 143, no. 2-3, pp. 551–557, 2003. View at Publisher · View at Google Scholar · View at Scopus
  12. M. Inc, M. Ergüt, and Y. Cherruault, “A different approach for solving singular two-point boundary value problems,” Kybernetes, vol. 34, no. 7-8, pp. 934–940, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. A. Ebaid, “A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 1914–1924, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. S. A. Khuri and A. Sayfy, “A novel approach for the solution of a class of singular boundary value problems arising in physiology,” Mathematical and Computer Modelling, vol. 52, no. 3-4, pp. 626–636, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Kumar and N. Singh, “Modified Adomian decomposition method and computer implementation for solving singular boundary value problems arising in various physical problems,” Computers and Chemical Engineering, vol. 34, no. 11, pp. 1750–1760, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. B. Jang, “Two-point boundary value problems by the extended Adomian decomposition method,” Journal of Computational and Applied Mathematics, vol. 219, no. 1, pp. 253–262, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. G. Adomian and R. Rach, “Inversion of nonlinear stochastic operators,” Journal of Mathematical Analysis and Applications, vol. 91, no. 1, pp. 39–46, 1983. View at Google Scholar · View at Scopus
  18. G. Adomian and R. Rach, “A new algorithm for matching boundary conditions in decomposition solutions,” Applied Mathematics and Computation, vol. 57, no. 1, pp. 61–68, 1993. View at Publisher · View at Google Scholar · View at Scopus
  19. G. Adomian and R. Rach, “Modified decomposition solution of linear and nonlinear boundary-value problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 23, no. 5, pp. 615–619, 1994. View at Publisher · View at Google Scholar · View at Scopus
  20. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, 1994.
  21. A. M. Wazwaz, “Approximate solutions to boundary value problems of higher order by the modified decomposition method,” Computers and Mathematics with Applications, vol. 40, no. 6-7, pp. 679–691, 2000. View at Publisher · View at Google Scholar · View at Scopus
  22. A. M. Wazwaz, “A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems,” Computers and Mathematics with Applications, vol. 41, no. 10-11, pp. 1237–1244, 2001. View at Publisher · View at Google Scholar · View at Scopus
  23. M. Benabidallah and Y. Cherruault, “Application of the Adomian method for solving a class of boundary problems,” Kybernetes, vol. 33, no. 1, pp. 118–132, 2004. View at Google Scholar · View at Scopus
  24. A. M. Wazwaz, “A new method for solving singular initial value problems in the second-order ordinary differential equations,” Applied Mathematics and Computation, vol. 128, no. 1, pp. 45–57, 2002. View at Publisher · View at Google Scholar · View at Scopus
  25. J. Duan and R. Rach, “A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations,” Applied Mathematics and Computation, vol. 218, no. 8, pp. 4090–4118, 2011. View at Publisher · View at Google Scholar
  26. K. Abbaoui and Y. Cherruault, “Convergence of Adomian's method applied to differential equations,” Computers and Mathematics with Applications, vol. 28, no. 5, pp. 103–109, 1994. View at Publisher · View at Google Scholar · View at Scopus
  27. Y. Cherruault, “Convergence of Adomian's method,” Kybernetes, vol. 18, no. 2, pp. 31–38, 1989. View at Publisher · View at Google Scholar
  28. M. M. Hosseini and H. Nasabzadeh, “On the convergence of Adomian decomposition method,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 536–543, 2006. View at Publisher · View at Google Scholar · View at Scopus