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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 232698, 9 pages
http://dx.doi.org/10.1155/2012/232698
Research Article

Using Lie Symmetry Analysis to Solve a Problem That Models Mass Transfer from a Horizontal Flat Plate

Department of Applied Mathematics, Walter Sisulu University, Private Bag X1, Mthatha 5117, South Africa

Received 16 July 2012; Revised 5 November 2012; Accepted 30 November 2012

Academic Editor: Hung Nguyen-Xuan

Copyright © 2012 W. Sinkala and M. Chaisi. 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. H. Fatoorehchi and H. Abolghasemi, “Adomian decomposition method to study mass transfer from a horizontal flat plate subject to laminar fluid flow,” Advances in Natural and Applied Sciences, vol. 5, no. 1, pp. 26–33, 2011.
  2. G. W. Bluman and S. Kumei, Symmetries and Differential Equations, vol. 81 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989. View at Zentralblatt MATH
  3. B. J. Cantwell, Introduction to Symmetry Analysis, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, UK, 2002.
  4. P. J. Olver, Applications of Lie Groups to Differential Equations, vol. 107 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2nd edition, 1993. View at Publisher · View at Google Scholar
  5. L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, NY, USA, 1982.
  6. H. Stephani, Differential Equations, Cambridge University Press, Cambridge, UK, 1989.
  7. G. Baumann, Symmetry Analysis of Differential Equations with Mathematica, Springer, New York, NY, USA, 2000. View at Zentralblatt MATH
  8. A. K. Head, “LIE, a PC program for Lie analysis of differential equations,” Computer Physics Communications, vol. 77, no. 2, pp. 241–248, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. W. Hereman, “Review of symbolic software for the computation of Lie symmetries of differential equations,” Euromath Bulletin, vol. 1, no. 2, pp. 45–82, 1994. View at Zentralblatt MATH
  10. F. Schwarz, “Automatically determining symmetries of partial differential equations,” Computing, vol. 34, no. 2, pp. 91–106, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. F. Schwarz, “Automatically determining symmetries of partial differential equations,” Computing, vol. 36, pp. 279–280, 1986.
  12. F. Schwarz, “Symmetries of differential equations: from Sophus Lie to computer algebra,” SIAM Review, vol. 30, no. 3, pp. 450–481, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. J. Sherring, A. K. Head, and G. E. Prince, “Dimsym and LIE: symmetry determination packages,” Mathematical and Computer Modelling, vol. 25, no. 8-9, pp. 153–164, 1997, Algorithms and software for symbolic analysis of nonlinear system. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. N. C. Caister, J. G. O'Hara, and K. S. Govinder, “Solving the Asian option PDE using Lie symmetry methods,” International Journal of Theoretical and Applied Finance, vol. 13, no. 8, pp. 1265–1277, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. R. K. Gazizov and N. H. Ibragimov, “Lie symmetry analysis of differential equations in finance,” Nonlinear Dynamics, vol. 17, no. 4, pp. 387–407, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. C. M. Khalique and A. Biswas, “Optical solitons with power law nonlinearity using Lie group analysis,” Physics Letters, Section A, vol. 373, no. 23-24, pp. 2047–2049, 2009. View at Publisher · View at Google Scholar
  17. K. P. Pereira, “Transformation groups applied to two-dimensional boundary value problems in fluid mechanics,” Journal of Nonlinear Mathematical Physics, vol. 15, supplement 1, pp. 192–202, 2008. View at Publisher · View at Google Scholar
  18. N. H. Ibragimov, Modern Group Analysis, Springer, Dordrecht, The Netherlands, 2000.
  19. V. Naicker, K. Andriopoulos, and P. G. L. Leach, “Symmetry reductions of a Hamilton-Jacobi-Bellman equation arising in financial mathematics,” Journal of Nonlinear Mathematical Physics, vol. 12, no. 2, pp. 268–283, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. W. Sinkala, P. G. L. Leach, and J. G. O'Hara, “Zero-coupon bond prices in the Vasicek and CIR models: their computation as group-invariant solutions,” Mathematical Methods in the Applied Sciences, vol. 31, no. 6, pp. 665–678, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. W. Sinkala, “Two ways to solve, using Lie group analysis, the fundamental valuation equation in the double-square-root model of the term structure,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 56–62, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH