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Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 98602, 15 pages
http://dx.doi.org/10.1155/2007/98602
Research Article

Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems

Department of Mathematics, Faculty of Science, COMSATS Institute of Information Technology, Islamabad, Pakistan

Received 3 July 2006; Revised 19 September 2006; Accepted 20 September 2006

Academic Editor: Nasiruddin Ahmed

Copyright © 2007 Syed Tauseef Mohyud-Din and Muhammad Aslam Noor. 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. A. H. Nayfeh, Introduction to Perturbation Techniques, John Wiley & Sons, New York, 1981. View at Zentralblatt MATH · View at MathSciNet
  2. A. H. Nayfeh, Problems in Perturbation, John Wiley & Sons, New York, 1985. View at Zentralblatt MATH · View at MathSciNet
  3. S. J. Liao, “An approximate solution technique not depending on small parameters: a special example,” International Journal of Non-Linear Mechanics, vol. 30, no. 3, pp. 371–380, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. J. Liao, “Boundary element method for general nonlinear differential operators,” Engineering Analysis with Boundary Elements, vol. 20, no. 2, pp. 91–99, 1997. View at Publisher · View at Google Scholar
  5. J.-H. He, “Approximate solution for nonlinear differential equations with convolution product nonlinearities,” Computer Methods in Applied Mechanics and Engineering, vol. 167, no. 1-2, pp. 69–73, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. J.-H. He, “Variational iteration method: a kind of nonlinear 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
  7. 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 MathSciNet
  8. M. A. Noor and S. Tauseef Mohyud-Din, “An efficient method for fourth-order boundary value problems,” to appear in Computers & Mathematics with Applications.
  9. M. A. Noor and S. Tauseef Mohyud-Din, “An efficient algorithm for solving fifth-order boundary value problems,” to appear in Mathematical and Computer Modelling.
  10. M. M. Chawla and C. P. Katti, “Finite difference methods for two-point boundary value problems involving high order differential equations,” BIT, vol. 19, no. 1, pp. 27–33, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. E. J. Doedel, “Finite difference collocation methods for nonlinear two-point boundary value problems,” SIAM Journal on Numerical Analysis, vol. 16, no. 2, pp. 173–185, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. T. F. Ma and J. da Silva, “Iterative solutions for a beam equation with nonlinear boundary conditions of third order,” Applied Mathematics and Computation, vol. 159, no. 1, pp. 11–18, 2004. View at Publisher · View at Google Scholar · View at MathSciNet