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Abstract and Applied Analysis
Volume 2014, Article ID 495734, 6 pages
http://dx.doi.org/10.1155/2014/495734
Research Article

Constructing Uniform Approximate Analytical Solutions for the Blasius Problem

Department of Statistics and Computer Science, Kunsan National University, Gunsan 573-701, Republic of Korea

Received 17 November 2013; Revised 5 February 2014; Accepted 6 February 2014; Published 12 March 2014

Academic Editor: Lucas Jodar

Copyright © 2014 Beong In Yun. 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. J. P. Boyd, “The Blasius function: computations before computers, the value of tricks, undergraduate projects, and open research problems,” SIAM Review, vol. 50, no. 4, pp. 791–804, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Finch, “Prandtl-Blasius flow,” 2008, http://www.people.fas.harvard.edu/~sfinch/csolve/bla.pdf.
  3. H. Schlichting, Boundary-Layer Theory, McGraw-Hill, New York, NY, USA, 7th edition, 1979. View at MathSciNet
  4. G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. Adomian, “Solution of the Thomas-Fermi equation,” Applied Mathematics Letters, vol. 11, no. 3, pp. 131–133, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. F. M. Allan and M. I. Syam, “On the analytic solutions of the nonhomogeneous Blasius problem,” Journal of Computational and Applied Mathematics, vol. 182, no. 2, pp. 362–371, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Biazar, M. Gholami Porshokuhi, and B. Ghanbari, “Extracting a general iterative method from an Adomian decomposition method and comparing it to the variational iteration method,” Computers & Mathematics with Applications, vol. 59, no. 2, pp. 622–628, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. P. Boyd, “The Blasius function in the complex plane,” Experimental Mathematics, vol. 8, no. 4, pp. 381–394, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. B. K. Datta, “Analytic solution for the Blasius equation,” Indian Journal of Pure and Applied Mathematics, vol. 34, no. 2, pp. 237–240, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J.-H. He, “Approximate analytical solution of Blasius' equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 3, no. 4, pp. 260–263, 1998. View at Publisher · View at Google Scholar · View at Scopus
  11. J.-H. He, “A review on some new recently developed nonlinear analytical techniques,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 1, no. 1, pp. 51–70, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J.-H. He, “A simple perturbation approach to Blasius equation,” Applied Mathematics and Computation, vol. 140, no. 2-3, pp. 217–222, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. 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
  14. J.-H. He, “Homotopy perturbation method for solving boundary value problems,” Physics Letters A, vol. 350, no. 1-2, pp. 87–88, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. 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
  16. S.-J. Liao, “An explicit, totally analytic approximate solution for Blasius' viscous flow problems,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 759–778, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J. Lin, “A new approximate iteration solution of Blasius equation,” Communications in Nonlinear Science & Numerical Simulation, vol. 4, no. 2, pp. 91–94, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. J. Parlange, R. D. Braddock, and G. Sander, “Analytical approximations to the solution of the Blasius equation,” Acta Mechanica, vol. 38, no. 1-2, pp. 119–125, 1981. View at Publisher · View at Google Scholar
  19. Ö. Savaş, “An approximate compact analytical expression for the Blasius velocity profile,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 10, pp. 3772–3775, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. A.-M. Wazwaz, “The variational iteration method for solving two forms of Blasius equation on a half-infinite domain,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 485–491, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. B. I. Yun, “Intuitive approach to the approximate analytical solution for the Blasius problem,” Applied Mathematics and Computation, vol. 215, no. 10, pp. 3489–3494, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. B. I. Yun, “Approximate analytical solutions using hyperbolic functions for the generalized Blasius problem,” Abstract and Applied Analysis, vol. 2012, Article ID 581453, 10 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. W. Bao and J. Shen, “A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates,” Journal of Computational Physics, vol. 227, no. 23, pp. 9778–9793, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. J. Shen and L.-L. Wang, “Some recent advances on spectral methods for unbounded domains,” Communications in Computational Physics, vol. 5, no. 2–4, pp. 195–241, 2009. View at Google Scholar · View at MathSciNet
  25. K. Parand, M. Shahini, and M. Dehghan, “Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type,” Journal of Computational Physics, vol. 228, no. 23, pp. 8830–8840, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. K. Parand, M. Dehghan, A. R. Rezaei, and S. M. Ghaderi, “An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method,” Computer Physics Communications, vol. 181, no. 6, pp. 1096–1108, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. K. Parand, M. Dehghan, and A. Taghavi, “Modified generalized Laguerre function tau method for solving laminar viscous flow: the Blasius equation,” International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20, no. 6-7, pp. 728–743, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  28. M. Dehghan and A. Saadatmandi, “A tau method for the one-dimensional parabolic inverse problem subject to temperature overspecification,” Computers & Mathematics with Applications, vol. 52, no. 6-7, pp. 933–940, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. A. Saadatmandi and M. Dehghan, “Numerical solution of a mathematical model for capillary formation in tumor angiogenesis via the tau method,” Communications in Numerical Methods in Engineering with Biomedical Applications, vol. 24, no. 11, pp. 1467–1474, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet