Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems
Syed Tauseef Mohyud-Din1and Muhammad Aslam Noor1
Academic Editor: Nasiruddin Ahmed
Received03 Jul 2006
Revised19 Sept 2006
Accepted20 Sept 2006
Published26 Dec 2006
Abstract
We apply the homotopy perturbation method for solving the
fourth-order boundary value problems. The analytical results of the boundary value
problems have been obtained in terms of convergent series with easily computable
components. Several examples are given to illustrate the efficiency and implementation of
the homotopy perturbation method. Comparisons are made to confirm the reliability of the
method. Homotopy method can be considered an alternative method to Adomian
decomposition method and its variant forms.
References
A. H. Nayfeh, Introduction to Perturbation Techniques, John Wiley & Sons, New York, 1981.
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.
S. J. Liao, “Boundary element method for general nonlinear differential operators,” Engineering Analysis with Boundary Elements, vol. 20, no. 2, pp. 91–99, 1997.
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.
M. A. Noor and S. Tauseef Mohyud-Din, “An efficient method for fourth-order boundary value problems,” to appear in Computers & Mathematics with Applications.
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.
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.
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.
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.