454
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

A comparison of the adomian and homotopy perturbation methods in solving the problem of squeezing flow between two circular plates

, , &
Pages 491-504 | Received 08 Feb 2010, Published online: 10 Feb 2011

References

  • Adomian , G. 1992 . A review of the decomposition method and some recent results for nonlinear equation . Mathematical and Computer Modelling , 13 (7) : 17 – 43 . doi:10.1016/0895–7177 (90)90125–7.
  • Biazar , J. , Ansari , R. , Hosseini , K. and Gholamin , P. 2008 . Solution of the linear and non‐linear Schrödinger equations using homotopy perturbation and Adomian decomposition methods . International Mathematical Forum , 38 : 1891 – 1897 .
  • Bujurke , N.M. and Kudenatti , R.B. 2007 . MHD lubrication flow between rough rectangular plates . Fluid Dynamics Research , 39 : 334 – 345 . doi:10.1016/j.fluiddyn.2006.05.004.
  • Cherruault , Y. and Adomian , G. 1993 . Decomposition methods: A new proof of convergence . Mathematical and Computer Modelling , 18 (12) : 103 – 106 . doi:10.1016/0895–7177 (93)90233‐O.
  • Estep , D. 2002 . Practical Analysis in One Variable. , New York : Springer‐Verlag . Inc,
  • Grimm , R.J. 1976 . Squeezing flows of Newtonian liquid films an analysis include the fluid inertia . Appl Sci Res , 32 : 146 – 149 . doi:10.1007/BF00383711.
  • Gupta , P.S. and Gupta , A.S. 1977 . Squeezing flow between parallel plates . Wear , 45 : 177 – 185 .
  • He , J.H. 1999 . Homotopy perturbation technique . Computer Methods in Applied Mechanics and Engineering , 178 : 257 – 262 . doi:10.1016/S0045–7825 (99)00018–3.
  • He , J.H. 2006 . Homotopy perturbation method for solving boundary value problems . Physics Letters , A 350 (1–2) : 87 – 88 . doi:10.1016/j.physleta.2005.10.005.
  • He , J.H. 2006 . Some asymptotic methods for strongly nonlinear equations . International Journal of Modern Physics , B 20 : 1141 – 1199 .
  • He , J.H. 2008 . Recent development of the homotopy perturbation method . Topological Methods in Nonlinear Analysis , 31 : 205 – 209 .
  • Ishizawa , S. 1976 . Squeezing flows of Newtonian liquid films an analysis include the fluid inertia . Appl Sci Res , 32 : 149 – 166 . doi:10.1007/BF00383711.
  • Jackson , J.D. 1963 . A study of squeezing flow . Appl Sci Res A11 , : 148 – 52 .
  • Jang , Bongsoo . 2008 . Two‐point boundary value problems by the extended Adomian decomposition method . Journal of Computational and Applied Mathematics , 219 : 253 – 262 . doi:10.1016/j.cam.2007.07.036.
  • Kokini , J.L. and Cussler , E.L. 1987 . “ The psychophysics of fluid food texture ” . In Food Texture: Instrumental and Sensory Measurement , Edited by: Moskowitz , H. 97 – 127 . Dekker .
  • Kokini , J.L. , Kadane , J.B. and Cussler , E.L. 1977 . Liquid texture perceived in the mouth . J. Texture Stud. , 8 : 195 – 218 . doi:10.1111/j.1745–4603.1977.tb01175.x.
  • Kuzma , D.C. 1967 . Fluid inertia effects in squeeze films . Appl Sci Res , 18 : 15 – 20 . doi:10.1007/BF00382330.
  • Laun , H.M. and Hassager , Rady M. 1999 . Analytical solutions for squeeze flow with partial wall slip . J. Non‐Newtonian Fluid Mech , 81 : 1 – 15 . doi:10.1016/S0377–0257 (98)00083–4.
  • Mavoungou , T. 1994 . Convergence of Adomian's method and applications to non‐linear partial differential equations . Kybernetes , 21 (6) : 13 – 25 . doi:10.1108/eb005942.
  • Nayfeh , A.H. 1979 . Introduction to perturbation techniques , Wiley .
  • Nhan , P.T. 2000 . Squeeze flow of a viscoelastic solid . J. Non‐Newtonian Fluid Mech , 95 : 433 – 462 .
  • Nicosia , M.A. and Robbins , J. 2001 . The fluid mechanics of bolus ejection from the oral cavity . J. Biomech. , 34 (12) : 1537 – 1544 . doi:10.1016/S0021–9290 (01)00147–6.
  • Rashidi , M.M. and Dinarvand , S. 2009 . Purely analytic approximate solutions for steady three‐dimensional problem of condensation film on inclined rotating disk by homotopy analysis method . Nonlinear Analysis Real World Applications , 10 (4) : 2346 – 2356 . doi:10.1016/j.nonrwa.2008.04.018.
  • Rashidi , M.M. and Domairry , G. 2009 . New analytical solution of the three‐dimensional Navier‐Stokes equations . Modern Physics Letters , B 26 : 3147 – 3155 . doi:10.1142/S0217984909021193.
  • Rashidi , M.M. , Ganji , D.D. and Dinarvand , S. 2009 . Explicit analytical solutions of the generalized Burger and Burger‐Fisher equations by homotopy perturbation method . Numerical Methods for Partial Differential Equations , 25 (2) : 409 – 417 . doi:10.1002/num.20350.
  • Sadighi , D.D. and Ganji , A. 2008 . Analytical treatment of linear and nonlinear Schrödinger equations: A study with homotopy‐perturbation and Adomian decomposition methods . Physics letters , A 372 : 465 – 469 . doi:10.1016/j.physleta.2007.07.065.
  • Siddiqui , A.M. , Ansari , A.R. , Ahmad , A. and Ahmad , N. On Taylor's scraping problem and flow of a Sisko fluid . 14 (4) 515 – 529 . doi:10.3846/1392–6292.2009.14.515–529.
  • Siddiqui , A.M. , Irum , S. and Ansari , A. R. 2008 . Unsteady squeezing flow of a viscous MHD fluid between parallel plates, a solution using the homotopy perturbation method . Math. Model. Anal. , 13 (4) : 565 – 576 . doi:10.3846/1392–6292.2008.13.565–576.
  • Siddiqui , A.M. , Mahmood , R. and Ghori , Q.K. 2008 . Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane . Chaos, Solitons and Fractals , 35 : 140 – 147 . doi:10.1016/j.chaos.2006.05.026.
  • Siddiqui , A.M. , Zeb , A. , Ghori , Q.K. and Benharbit , A.M. 2008 . Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates . Chaos, Solitons and Fractals , 36 : 182 – 192 . doi:10.1016/j.chaos.2006.06.037.
  • Singh , P. and Verma , R.L. 1981 . Application of a thermodynamic method to squeezing flow between parallel plates . Wear , 65 : 375 – 383 .
  • Stefan , J. 1874 . Versuch U ber die scheinbare adhesion . Akad Wissensch Wien Math Natur , 69 : 713 – 721 .
  • Thrope , J.F. 1967 . Developments in theoretical and applied mechanics Vol.3 , Edited by: Shaw , W. A. Oxford : Pergamon .
  • Tichy , J. and Winner , W.O. 1970 . Inertial considerations in parallel circular squeeze film bearings . Trans ASME J Lub Technol , 92 : 588 – 592 .
  • Usha , R. and Sridharan , R. 1996 . Arbitrary squeezing of a viscous fluid between elliptic plates . Fluid Dynam Res , 18 : 35 – 51 .
  • Verma , R.L. 1981 . A numerical solution for squeezing flow between parallel channels . Wear , 72 : 89 – 95 .
  • Wang , C.Y. and Watson , L.T. 1979 . Squeezing of a viscous fluid between elliptic plates . Appl Sci Res , 35 : 195 – 207 . doi:10.1007/BF00382705.
  • Wazwaz , A.‐M. 2005 . Adomian decomposition method for a reliable treatment of the Bratu‐type equations . Applied Mathematics and Computation , 166 : 652 – 663 . doi:10.1016/j.amc.2004.06.059.
  • Wolfe , W.A. 1964–1965 . Squeeze film pressures . Appl Sci Res , 14 : 77 – 90 . doi:10.1007/BF00382232.
  • Wu , Lei , Xie , Li dan and Zhang , Jie fang . 2009 . Adomian decomposition method for nonlinear differential‐difference equations . Communications in Nonlinear Science and Numerical Simulation , 14 : 12 – 18 . doi:10.1016/j.cnsns.2007.01.007.
  • Yildirim , Turgut Oziso Ahmet . 2008 . Comparison between Adomian's method and He's homotopy perturbation method . Computers and Mathematics with Applications , 56 : 1216 – 1224 . doi:10.1016/j.camwa.2008.02.023.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.