About this Journal Submit a Manuscript Table of Contents
Advances in Mathematical Physics
Volume 2014 (2014), Article ID 410620, 6 pages
http://dx.doi.org/10.1155/2014/410620
Research Article

Application of Successive Linearisation Method to Squeezing Flow with Bifurcation

1School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa
2Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa
3Department of Mathematics & Applied Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received 28 September 2013; Accepted 16 December 2013; Published 2 January 2014

Academic Editor: R. N. Jana

Copyright © 2014 S. S. Motsa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. D. Bertram, “Unstable equilibrium behaviour in collapsible tubes,” Journal of Biomechanics, vol. 19, no. 1, pp. 61–69, 1986. View at Publisher · View at Google Scholar · View at Scopus
  2. J. D. Jackson, “A study of squeezing flow,” Applied Scientific Research A, vol. 11, no. 1, pp. 148–152, 1963. View at Publisher · View at Google Scholar · View at Scopus
  3. C. D. Bertram and T. J. Pedley, “A mathematical model of unsteady collapsible tube behaviour,” Journal of Biomechanics, vol. 15, no. 1, pp. 39–50, 1982. View at Publisher · View at Google Scholar · View at Scopus
  4. N. M. Bujurke, P. K. Achar, and N. P. Pai, “Computer extended series for squeezing flow between plates,” Fluid Dynamics Research, vol. 16, no. 2-3, pp. 173–187, 1995. View at Publisher · View at Google Scholar · View at Scopus
  5. O. D. Makinde, T. G. Motsumi, and M. P. Ramollo, “Squeezing flow between parallel plates: a bifurcation study,” Far East Journal of Applied Mathematics, vol. 9, no. 2, pp. 81–94, 2002. View at MathSciNet
  6. C. Y. Wang, “Squeezing of fluid between two plates,” ASME Journal of Applied Mechanics, vol. 43, no. 4, pp. 579–583, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. S. Ishizawa, “The unsteady flow between two parallel discs with arbitrary varying gap width,” Bulletin of JSME, vol. 9, no. 35, pp. 533–550, 1966. View at Publisher · View at Google Scholar
  8. O. D. Makinde, “Fluid dynamics of parallel plates viscometer: a case study of methods of series summation,” Quaestiones Mathematicae, vol. 26, no. 4, pp. 405–417, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Abbasbandy and T. Hayat, “Solution of the MHD Falkner-Skan flow by homotopy analysis method,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 9-10, pp. 3591–3598, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, vol. 2 of Modern Mechanics and Mathematics, Chapman & Hall/CRC Press, 2003. View at MathSciNet
  11. S.-J. Liao, “A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate,” Journal of Fluid Mechanics, vol. 385, pp. 101–128, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J.-H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J.-H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  14. S. S. Motsa, P. Sibanda, and S. Shateyi, “A new spectral-homotopy analysis method for solving a nonlinear second order BVP,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 9, pp. 2293–2302, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. S. S. Motsa, P. Sibanda, F. G. Awad, and S. Shateyi, “A new spectral-homotopy analysis method for the MHD Jeffery-Hamel problem,” Computers & Fluids, vol. 39, no. 7, pp. 1219–1225, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J.-H. He, “Variational iteration method—a kind of non-linear analytical technique: some examples,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 699–708, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. S. S. Motsa and S. Shateyi, “A successive linearization method approach to solve Lane-Emden type of equations,” Mathematical Problems in Engineering, vol. 2012, Article ID 280702, 14 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Z. G. Makukula, P. Sibanda, S. S. Motsa, and S. Shateyi, “On new numerical techniques for the MHD flow past a shrinking sheet with heat and mass transfer in the presence of a chemical reaction,” Mathematical Problems in Engineering, vol. 2011, Article ID 489217, 19 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. S. S. Motsa and S. Shateyi, “Successive linearisation analysis of unsteady heat and mass transfer from a stretching surface embedded in a Porous medium with suction/injection and thermal radiation effects,” Canadian Journal of Chemical Engineering, vol. 90, no. 5, pp. 1323–1335, 2011. View at Publisher · View at Google Scholar
  20. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer, Berlin, Germany, 1988. View at MathSciNet
  21. L. N. Trefethen, Spectral Methods in MATLAB, vol. 10 of Software, Environments, and Tools, SIAM, Philadelphia, Pa, USA, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  22. J. Kierzenka and L. F. Shampine, “A BVP solver based on residual control and the MATLAB PSE,” ACM Transactions on Mathematical Software, vol. 27, no. 3, pp. 299–316, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  23. L. F. Shampine, I. Gladwell, and S. Thompson, Solving ODEs with MATLAB, Cambridge University Press, Cambridge, UK, 2003. View at MathSciNet