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Journal of Mathematics
Volume 2013, Article ID 720134, 4 pages
http://dx.doi.org/10.1155/2013/720134
Research Article

Variational Iteration Method for Nonlinear Singular Two-Point Boundary Value Problems Arising in Human Physiology

Department of Mathematics and Statistics, American University of Sharjah, P.O. Box 26666, Sharjah, UAE

Received 15 November 2012; Accepted 13 December 2012

Academic Editor: Jen-Chih Yao

Copyright © 2013 Marwan Abukhaled. 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. J. H. He, “Variational iteration method—a kind of non-linear analytical technique: some examples,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 699–708, 1999. View at Publisher · View at Google Scholar · View at Scopus
  2. J.-H. He, “Variational iteration method—some recent results and new interpretations,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 3–17, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. 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
  4. J. A. Adam, “A simplified mathematical model of tumor growth,” Mathematical Biosciences, vol. 81, no. 2, pp. 229–244, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. H. P. Greenspan, “Models for the growth of a solid tumor by diffusion,” Studies in Applied Mathematics, vol. 4, pp. 317–340, 1972. View at Google Scholar · View at Zentralblatt MATH
  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 Publisher · 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 Publisher · View at Google Scholar · View at Scopus
  8. N. S. Asaithambi and J. B. Garner, “Pointwise solution bounds for a class of singular diffusion problems in physiology,” Applied Mathematics and Computation, vol. 30, no. 3, pp. 215–222, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. M. Abukhaled, S. A. Khuri, and A. Sayfy, “A numerical approach for solving a class of singular boundary value problems arising in physiology,” International Journal of Numerical Analysis and Modeling, vol. 8, no. 2, pp. 353–363, 2011. View at Google Scholar · View at Zentralblatt MATH
  10. A. M. Wazwaz, “The variational iteration method for solving nonlinear singular boundary value problems arising in various physical models,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 10, pp. 3881–3886, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. A. S. V. Ravi Kanth and K. Aruna, “He's variational iteration method for treating nonlinear singular boundary value problems,” Computers & Mathematics with Applications, vol. 60, no. 3, pp. 821–829, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. J. He, “Variational iteration method for delay differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 2, no. 4, pp. 235–236, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. J.-H. He, “Variational iteration method for autonomous ordinary differential systems,” Applied Mathematics and Computation, vol. 114, no. 2-3, pp. 115–123, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. J.-H. He, “Variational principles for some nonlinear partial differential equations with variable coefficients,” Chaos, Solitons & Fractals, vol. 19, no. 4, pp. 847–851, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. Z. M. Odibat and S. Momani, “Application of variational iteration method to nonlinear differential equations of fractional order,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 1, pp. 27–34, 2006. View at Google Scholar · View at Scopus
  17. S. Momani and Z. Odibat, “Numerical comparison of methods for solving linear differential equations of fractional order,” Chaos, Solitons & Fractals, vol. 31, no. 5, pp. 1248–1255, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. J. Lu, “Variational iteration method for solving two-point boundary value problems,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 92–95, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. J. H. He, “Asymptotic methods for solitary solutions and compactons,” Abstract and Applied Analysis, vol. 2012, Article ID 916793, 130 pages, 2012. View at Google Scholar
  20. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, USA, 1972.
  21. D. Khojasteh Salkuyeh, “Convergence of the variational iteration method for solving linear systems of ODEs with constant coefficients,” Computers & Mathematics with Applications, vol. 56, no. 8, pp. 2027–2033, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH