THERMAL SCIENCE
International Scientific Journal
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A NOTE ON THE HOMOTOPY PERTURBATION METHOD
ABSTRACT
The homotopy perturbation method admits some unknown parameters in the obtained series solutions, which can be identified after few iteration steps using the method of least squares. The solution procedure of the so-called optimal homotopy asymptotic method follows the same way.
KEYWORDS
PAPER SUBMITTED: 2010-01-30
PAPER ACCEPTED: 2010-01-30
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REFERENCES
[1] Marinca, V., Herisanu, N., Nemes, I., An Optimal Homotopy Asymptotic Method with Application to Thin Film Flow, Central European Journal of Physics, 6 (2008), 3, pp. 648-653
[2] Babaelahi, M., Ganji, D. D., Joneidi, A. A., Analytical Treatment of Mixed Convection Flow Past Vertical Flat Plate, Thermal Science, 14 (2010), 2, pp. 409-416
[3] He, J.-H., A Coupling Method of a Homotopy Technique and a Perturbation Technique for Non-Linear Problems, Int. J. Nonlinear Mech., 35 (2000), 1, pp. 37-43
[4] He, J.-H., Some Asymptotic Methods for Strongly Nonlinear Equations, Int. J. Mod. Phys. B, 20 (2006), 10, pp. 1141-1199
[5] He, J.-H., An Elementary Introduction to Recently Developed Asymptotic Methods and Nanomechanics in Textile Engineering, Int. J. of Mod. Phys. B, 22 (2008), 21, pp. 3487-3578
[6] He, J.-H., Recent Development of the Homotopy Perturbation Method, Topological Methods in Non-Linear Analysis, 31 (2008), 2, pp. 205-209
[7] He, J.-H., New Interpretation of Homotopy Perturbation Method, Int. J. Mod. Phys. B, 20 (2006), 18, pp. 2561-2568
[8] He, J.-H., Modified Lindstedt-Poincare Methods for Some Strongly Non-Linear Oscillations Part I: Expansion of a Constant, Int. J. Nonlinear Mech., 37 (2002), 2, pp. 309-314
[9] Xu, L., Application of He's Parameter-Expansion Method to an Oscillation of a Mass Attached to a Stretched Elastic Wire, Phys. Lett. A, 368 (2007), 3-4, pp. 259-262
[10] Xu, L., Determination of Limit Cycle by He's Parameter-Expanding Method for Strongly Nonlinear Oscillators, J. Sound Vib., 302 (2007), 1-2, pp. 178-184
[11] Sweilam, N. H., Al-Bar, R. F., Implementation of the Parameter-Expansion Method for the Coupled Van der Pol Oscillators, Int. J. Nonlin. Sci. Num., 10 (2009), 2, pp. 259-264
[12] Sweilam, N. H., Khader, M. M., Application of He's Parameter-Expansion Method for the Nonlinear Differential Equations, Int. J. Nonlin. Sci. Num., 10 (2009), 2, pp. 265-272
[13] Shin, B. C., Darvishi, M. T., Karami, A., Application of He's Parameter-Expansion Method to a Nonlinear Self-Excited Oscillator System, Int. J. Nonlin. Sci. Num., 10 (2009), 2, pp. 137-143
[14] Zengin, F. O., Kaya, M. O., Demirbag, S. A., Application of Parameter-Expansion Method to Nonlinear Oscillators with Discontinuities, Int. J. Nonlin. Sci. Num., 9 (2008), 1, pp. 267-270
[15] Ariel, P. D., Homotopy Perturbation Method and the Natural Convection Flow of a Third Grade Fluid through a Circular Tube, Nonlinear Science Letters A, 1 (2010), 1, pp. 43-52
[16] He, J. H., An Elementary Introduction to the Homotopy Perturbation Method, Comput. & Maths. with Application, 57 (2009), 3, pp. 410-412.
[17] Marinca, V., Herisanu, N., A Modified Variational Iteration Method for Strongly Nonlinear Problems, Nonlinear Science Letters A, 1 (2010), 2, pp. 183-192
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