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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 232698, 9 pages
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.
- 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.
- G. W. Bluman and S. Kumei, Symmetries and Differential Equations, vol. 81 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989.
- B. J. Cantwell, Introduction to Symmetry Analysis, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, UK, 2002.
- 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.
- L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, NY, USA, 1982.
- H. Stephani, Differential Equations, Cambridge University Press, Cambridge, UK, 1989.
- G. Baumann, Symmetry Analysis of Differential Equations with Mathematica, Springer, New York, NY, USA, 2000.
- A. K. Head, “LIE, a PC program for Lie analysis of differential equations,” Computer Physics Communications, vol. 77, no. 2, pp. 241–248, 1993.
- 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.
- F. Schwarz, “Automatically determining symmetries of partial differential equations,” Computing, vol. 34, no. 2, pp. 91–106, 1985.
- F. Schwarz, “Automatically determining symmetries of partial differential equations,” Computing, vol. 36, pp. 279–280, 1986.
- F. Schwarz, “Symmetries of differential equations: from Sophus Lie to computer algebra,” SIAM Review, vol. 30, no. 3, pp. 450–481, 1988.
- 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.
- 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.
- 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.
- 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.
- 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.
- N. H. Ibragimov, Modern Group Analysis, Springer, Dordrecht, The Netherlands, 2000.
- 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.
- 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.
- 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.