Nonlinear Dynamics

, Volume 50, Issue 1–2, pp 27–35 | Cite as

Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt

  • M. Sajid
  • T. Hayat
  • S. Asghar
Original Article


In this paper, we prove in general that the homotopy perturbation method (HPM) proposed in 1998 is only a special case of the homotopy analysis method (HAM) profound in 1992 when ħ = −1. Besides, by using the thin film flows of Sisko and Oldroyd 6-constant fluids on a moving belt as examples, we show that the solutions given by HPM (Siddiqui, A.M., Ahmed, M., Ghori, Q.K.: Chaos Solitons and Fractals (2006) in press) are divergent, and thus useless. However, by choosing a proper value of the auxiliary parameter ħ, we give convergent series solution by means of the HAM. These two examples also show that, different from the HPM and other traditional analytic techniques, the HAM indeed provides us with a simple way to ensure the convergence of the solution.


Sisko fluid Oldroyd 6-constant fluid Thin film flow HAM solution 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan
  2. 2.Physics Research DivisionPINSTECHIslamabadPakistan
  3. 3.COMSATS Institute of Information TechnologyIslamabadPakistan

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