THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Ji-Huan He

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
homotopy equation, parameter-expansion method, method of least squares
PAPER SUBMITTED: 2010-01-30
PAPER ACCEPTED: 2010-01-30
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2010, VOLUME 14, ISSUE Issue 2, PAGES [565 - 568]
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
PDF VERSION [DOWNLOAD]
A NOTE ON THE HOMOTOPY PERTURBATION METHOD

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence