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Homotopy perturbation method for solving fourth-order boundary value problems. (English) Zbl 1144.65311
Summary: We apply the homotopy perturbation method for solving fourth-order boundary value problems. The analytical results of the boundary value problems are 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. The homotopy method can be considered an alternative method to the Adomian decomposition method and its variant forms.

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
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References:
[1] A. H. Nayfeh, Introduction to Perturbation Techniques, John Wiley & Sons, New York, 1981. · Zbl 0449.34001
[2] A. H. Nayfeh, Problems in Perturbation, John Wiley & Sons, New York, 1985. · Zbl 0573.34001
[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. · Zbl 0837.76073
[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.
[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. · Zbl 0932.65143
[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. · Zbl 1342.34005
[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. · Zbl 1102.34039
[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. · Zbl 1141.65375
[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. · Zbl 1133.65052
[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. · Zbl 0401.65053
[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. · Zbl 0438.65068
[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. · Zbl 1095.74018
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