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Journal of Applied Mathematics
Volume 2013, Article ID 423628, 15 pages
http://dx.doi.org/10.1155/2013/423628
Research Article

A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa

Received 7 June 2013; Revised 9 August 2013; Accepted 9 August 2013

Academic Editor: Chein-Shan Liu

Copyright © 2013 S. S. Motsa. 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. A. A. Ahmed, “Similarity solution in MHD: effects of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a stretching surface considering suction or injection,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, pp. 2202–2214, 2009. View at Publisher · View at Google Scholar
  2. R. Cortell, “Numerical solutions of the classical Blasius flat-plate problem,” Applied Mathematics and Computation, vol. 170, pp. 706–710, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. Asaithambi, “A second-order finite-difference method for the Falkner-Skan equation,” Applied Mathematics and Computation, vol. 156, no. 3, pp. 779–786, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. H. B. Keller and T. Cebeci, “Accurate numerical methods for boundary layer flow-I. Two dimensional laminar flows,” in Proceedings of the 2nd International Conference on Numerical Methods in Fluid Dynamics, pp. 92–100, Berkeley, Calif, USA, 1971.
  5. T. Cebeci and P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer, Springer, New York, NY, USA, 1984. View at MathSciNet
  6. S. S. Motsa and P. Sibanda, “On the solution of MHD flow over a nonlinear stretching sheet by an efficient semi-analytical technique,” International Journal for Numerical Methods in Fluids, vol. 68, pp. 1524–1537, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  7. S. S. Motsa, S. Shateyi, and P. Sibanda, “A model of steady viscous flow of a micropolar fluid driven by injection or suction between a porous disk and a non-porous disk using a novel numerical technique,” The Canadian Journal of Chemical Engineering, vol. 88, no. 6, pp. 991–1002, 2010. View at Google Scholar
  8. R. Sharma, R. Bhargava, and P. Bhargava, “A numerical solution of unsteady MHD convection heat and mass transfer past a semi-infnite vertical porous moving plate using element free galerkin method,” Computational Material Science, vol. 48, pp. 537–543, 2010. View at Google Scholar
  9. V. B. Mandelzweig and F. Tabakin, “Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs,” Computer Physics Communications, vol. 141, pp. 268–281, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Zhu, Q. Wu, and X. Cheng, “Numerical solution of the Falkner-Skan equation based on quasilinearization,” Applied Mathematics and Computation, vol. 215, no. 7, pp. 2472–2485, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. S. S. Motsa, T. Hayat, and O. M. Aldossary, “MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method,” Applied Mathematics and Mechanics, vol. 33, no. 8, pp. 975–990, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. S. Motsa and S. Shateyi, “Successive linearization analysis of the effects of partial slip, thermal diffusion, and diffusion-thermo on steady MHD convective flow due to a rotating disk,” Mathematical Problems in Engineering, vol. 2012, Article ID 397637, 15 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. F. G. Awad, P. Sibanda, S. S. Motsa, and O. D. Makinde, “Convection from an inverted cone in a porous medium with cross-diffusion effects,” Computers & Mathematics with Applications, vol. 61, no. 5, pp. 1431–1441, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. 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
  15. 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
  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 MathSciNet
  17. A. Alizadeh-Pahlavan and S. Borjian-Boroujeni, “On the analytical solution of viscous fluid flow past a flat plate,” Physics Letters, vol. 372, pp. 3678–3682, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. J. H. He, “Approximate analytical solution of Blasius' equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 4, pp. 75–78, 1999. View at Google Scholar · View at Zentralblatt MATH
  19. 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
  20. B. Kuo, “Thermal boundary-layer problems in a semi-infinite flat plate by the differential transformation method,” Applied Mathematics and Computation, vol. 150, no. 2, pp. 303–320, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  21. M. M. Rashidi, “The modified differential transform method for solving MHD boundary-layer equations,” Computer Physics Communications, vol. 180, no. 11, pp. 2210–2217, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. L.-T. Yu and C.-K. Chen, “The solution of the Blasius equation by the differential transformation method,” Mathematical and Computer Modelling, vol. 28, no. 1, pp. 101–111, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. C.-W. Chang, J.-R. Chang, and C.-S. Liu, “The lie-group shooting method for solving classical Blasius flat-plate problem,” Computers, Materials, & Continua, vol. 7, no. 3, pp. 139–153, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. J. Lin, “A new approximate iteration solution of Blasius equation,” Communications in Nonlinear Science & Numerical Simulation, vol. 4, no. 2, pp. 91–99, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. A. 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
  26. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer, Berlin, Germany, 1988. View at MathSciNet
  27. L. N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, Pa, USA, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  28. R. E. Bellman and R. E. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems, Elsevier, New York, NY, USA, 1965. View at MathSciNet
  29. A. J. Chamkha, A. M. Aly, and M. A. Mansour, “Similarity solution for unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and chemical reaction effects,” Chemical Engineering Communications, vol. 197, pp. 846–858, 2010. View at Publisher · View at Google Scholar
  30. 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 effect,” The Canadian Journal of Chemical Engineering, vol. 90, no. 5, pp. 1323–1335, 2011. View at Publisher · View at Google Scholar
  31. J. P. Boyd, “The Blasius function: computations before computers, the value of tricks, undergraduate projects, and open research problems,” SIAM Review, vol. 50, pp. 791–804, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  32. B. D. Ganapol, “Highly accurate solutions of the Blasius and Falkner-Skan boundary layer equations via convergence acceleration,” http://arxiv.org/abs/1006.3888.
  33. L. F. Shampine, M. W. Reichelt, and J. Kierzenka, “Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c,” http://www.mathworks.com/bvp_tutorial.
  34. R. Krivec and V. B. Mandelzweig, “Numerical investigation of quasilinearization method in quantum mechanics,” Computer Physics Communications, vol. 138, pp. 69–79, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  35. V. B. Mandelzweig, “Quasilinearization method and its verification on exactly solvable models in quantum mechanics,” Journal of Mathematical Physics, vol. 40, no. 12, pp. 6266–6291, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  36. V. B. Mandelzweig, “Quasilinearization method: nonperturbative approach to physical problems,” Physics of Atomic Nuclei, vol. 68, no. 7, pp. 1227–1258, 2005. View at Publisher · View at Google Scholar
  37. W. S. Don and A. Solomonoff, “Accuracy and speed in computing the chebyshev collocation derivative,” SIAM Journal on Scientific Computing, vol. 16, no. 6, pp. 1253–1268, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet