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An efficient algorithm for solving fifth-order boundary value problems. (English) Zbl 1133.65052
Summary: We apply the homotopy perturbation method for solving fifth-order boundary value problems. The analytical results of the equations 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.

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
45F05 Systems of nonsingular linear integral equations
65R20 Numerical methods for integral equations
Full Text: DOI
[1] Caglar, H.N.; Caglar, S.H.; Twizell, E.E., The numerical solution of fifth order boundary-value problems with sixth degree B-spline functions, Appl. math. lett., 12, 25-30, (1999) · Zbl 0941.65073
[2] Davies, A.R.; Karageoghis, A.; Phillips, T.N., Spectral glarkien methods for the primary two-point boundary-value problems in modeling viscelastic flows, Internat. J. numer. methods engrg., 26, 647-662, (1988) · Zbl 0635.73091
[3] Fyfe, D.J., Linear dependence relations connecting equal interval \(N\)th degree splines and their derivatives, J. inst. math. appl., 7, 398-406, (1971) · Zbl 0219.65010
[4] He, J.H., Variational iteration method—a kind of nonlinear analytical technique: some examples, Internat. J. nonlinear mech., 34, 699-708, (1999) · Zbl 1342.34005
[5] He, J.H., Variational method for autonomous ordinary differential equations, Appl. math. comput., 114, 115-123, (2000) · Zbl 1027.34009
[6] He, J.H., Variational theory for linear magneto-electro-elasticity, Internat. J. nonlinear sci. numer. simul., 2, 4, 309-316, (2001) · Zbl 1083.74526
[7] He, J.H., Variational principle for some nonlinear partial differential equations with variable coefficients, Chaos soliton fractals, 19, 4, 847-851, (2004) · Zbl 1135.35303
[8] Inokuti, M.; Dekine, H.; Mura, T., General use of the Lagrange multiplier in nonlinear mathematical physics, (), 156-162
[9] Karageoghis, A.; Phillips, T.N.; Davies, A.R., Spectral collocation methods for the primary two-point boundary-value problems in modeling viscelastic flows, Internat. J. numer. methods engrg., 26, 805-813, (1998) · Zbl 0637.76008
[10] G.L. Liu, New research directions in singular perturbation theory: artificial parameter approach and inverse-perturbation technique, in: Proceeding of the Conference of the 7th Modern Mathematics and Mechanics, Shanghai, 1997
[11] Liao, S.J., An approximate solution technique not depending on small parameter: a special example, Internat. J. nonlinear mech., 30, 3, 371-380, (1995) · Zbl 0837.76073
[12] Liao, S.J., Boundary element method for general nonlinear differential operators, Eng. anal. boundary ement., 20, 2, 91-99, (1997)
[13] Nayfeh, A.H., Introduction to perturbation technique, (1981), John Wiley and Sons New York
[14] Nayfeh, A.H., Problems in perturbation, (1985), John Wiley and Sons New York · Zbl 0139.31904
[15] M. Aslam Noor, S.T. Mohyud-Din, Variational iteration technique for solving fifth-order boundary value problems, 2006 (preprint)
[16] Siraj-ul-Islam; Khan, M.A., A numerical method based on nonpolynomial sextic spline functions for the solution of special fifth-order boundary value problems, Appl. math. comput., 181, 356-361, (2006) · Zbl 1148.65312
[17] Wazwaz, A.M., The numerical solution of fifth-order boundary-value problems by Adomian decomposition, J. comput. appl. math., 136, 259-270, (2001) · Zbl 0986.65072
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