Homotopy perturbation method for solving fourth – order boundary value problems with additional boundary condition

Filipowska, Renata

doi:10.4467/2353737XCT.17.160.7172

Abstract

This paper presents the homotopy perturbation method for solving linear and non–linear two–point boundary value problems in the form of a fourth–order differential equation and five boundary conditions. Three initial and two final conditions were taken into account. The solution of this problem is possible only when the considered equation includes an unknown parameter. The presented method has been illustrated with a numerical example.

References

[1] Sung N.Ha., A nonlinear shooting method for two-point boundary value problems, Comp. and Math. with Appl., 42, 2001, 1411–1420.10.1016/S0898-1221(01)00250-4
Search in Google Scholar Back to article
[2] Filipowska R., An iterative shooting method for the solution of higher order boundary value problems with additional boundary conditions, Solid State Phenomena, 235, 2015, 31–36.10.4028/www.scientific.net/SSP.235.31
Search in Google Scholar Back to article
[3] Filipowska R., Variational iteration technique for solving higher order boundary value problem with additional boundary conditions, Technical Transactions, 4- M/2016, 15–20.
Search in Google Scholar Back to article
[4] Noor A.M., Mohyud–Din S.T., Variational iteration technique for solving higher-order boundary value problems, Applied Math. and Computation, 189, 2007, 1929–1942.10.1016/j.amc.2006.12.071
Search in Google Scholar Back to article
[5] He J.H., Wu X.H., Variational iteration method: New development and applications, Comp. and Math. with Appl., 54, 2007, 881–894.10.1016/j.camwa.2006.12.083
Search in Google Scholar Back to article
[6] Zhang J., The numerical solution of fifth-order boundary value problems by the variational iteration method, Com. and Math. with Appl., 58, 2009, 2347–2350.10.1016/j.camwa.2009.03.073
Search in Google Scholar Back to article
[7] Noor A.M., Mohyud-Din S.T., An efficient algorithm for solving fifth-order boundary value problems, Math. and Comp. Modelling, 45, 2007, 954–964.10.1016/j.mcm.2006.09.004
Search in Google Scholar Back to article
[8] Chun Ch., Sakthivel R., Homotopy perturbation technique for solving two-point boundary value problems–comparison with other methods, Comp. Physics Communications, 181, 2010, 1021–1024.10.1016/j.cpc.2010.02.007
Search in Google Scholar Back to article
[9] Hetmaniok E., Słota D., Wróbel A., Zielonka A., Application of the homotopy perturbation method for the systems of Volterra integral equations, Zesz. Nauk. PŚ, Mat. Stosow., 5, 2015, 71–77.
Search in Google Scholar Back to article
[10] He J.H., Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng., 178, 1999, 257–262.10.1016/S0045-7825(99)00018-3
Search in Google Scholar Back to article
[11] Nayfeh A.H., Introduction to Perturbation Technique, John Wiley and Sons, New York 1981.
Search in Google Scholar Back to article

Homotopy perturbation method for solving fourth – order boundary value problems with additional boundary condition

Abstract

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