Numerical Comparison of Methods for Solving Boundary Layer Problems in Hydrodynamics

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This paper presents a numerical comparison between the differential transform method and the modified Adomian decomposition method for solving the boundary layer problems arising in hydrodynamics. The results show that the differential transform method and modified Adomian decomposition method are easier and more reliable to use in solving this type of problem and provides accurate data as compared with those obtained by other numerical methods.

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508-512

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January 2013

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© 2013 Trans Tech Publications Ltd. All Rights Reserved

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[1] S. Goldstein, Concerning some solutions of the boundary layer equations in hydrodynamics, Proc. Cambridge Phil. Soc. 26 (1930), 1-30.

DOI: 10.1017/s0305004100014997

Google Scholar

[2] V. M. Falkner and S. W. Skan, Some approximations of the boundary-layer equations, Phil. Mag. 12 (1931), 865-896.

Google Scholar

[3] D. R. Hartree, On an equation ocuuring in Falkner and Skan's approximate treatment of the equations of the boundary layer, Proc. Cambridge Phil. Soc. 33 (1937), 223-239.

DOI: 10.1017/s0305004100019575

Google Scholar

[4] L. Howarth, On the solution of the laminar boundary layer equation, Proc. Royal Soc. of London A. 164 (1937), 547-579.

Google Scholar

[5] T. Cebeci and H. B. Keller, Shooting and parallel shooting methods for solving the Falkner-Skan boundary-layer equation, J. Comput. Phys. 7 (1971), 289-300.

DOI: 10.1016/0021-9991(71)90090-8

Google Scholar

[6] S. Kakac and Y. Yener, Convective Heat Transfer, Second ed., CRC, Boca Raton, FL, (1995).

Google Scholar

[7] A. Asaithambi, A finite-difference method for the Falkner-Skan equation, Appl. Math. Comput. 92 (1998), 135-141.

DOI: 10.1016/s0096-3003(97)10042-x

Google Scholar

[8] L. Wang, A new algorithm for solving classical Blasius equation, Appl. Math. Comput. 157 (2004), 1-9.

Google Scholar

[9] I. Hashim, Comments on A new algorithm for solving classical Blasius equation, by L. Wang, Appl. Math. Comput. 176 (2006), 700-703.

DOI: 10.1016/j.amc.2005.10.016

Google Scholar

[10] J. K. Zhou, Differential Transformation and Its Application for Electrical Circuits, Huazhong University Press, Wuhan, China 1986 (in Chinese).

Google Scholar

[11] M. J. Jang and C. L. Chen, Analysis of the response of a strongly nonlinear damped system using a differential transformation technique, Appl. Math. Comput. 88 (1997), 137-151.

DOI: 10.1016/s0096-3003(96)00308-6

Google Scholar

[12] S. H. Chang and I. L. Chang, A new algorithm for calculating one-dimensional differential transform of nonlinear functions, Appl. Math. Comput. 195 (2008), 799-808.

DOI: 10.1016/j.amc.2007.05.026

Google Scholar

[13] S. H. Chang and I. L. Chang, A new algorithm for calculating two-dimensional differential transform of nonlinear functions, Appl. Math. Comput. 215 (2009), 2486-2494.

DOI: 10.1016/j.amc.2009.08.046

Google Scholar

[14] S. H. Chang and I. L. Chang, An efficient method for solving Troesch's problem, Adv. Sci. Lett. 9 (2012), 920-924.

Google Scholar

[15] A. M. Wazwaz, A reliable modification of Adomian's decomposition method, Appl. Math. Comput. 102 (1999), 77-86.

Google Scholar

[16] A. M. Wazwaz, The modified decomposition method and the Pade' approximats for solving Thomas-Fermi equation, Appl. Math. Comput. 105 (1999), 11-19.

Google Scholar

[17] A. M. Wazwaz, The decomposition method applied to systems of partial differential equations and to the reaction–diffusion Brusselator model, Appl. Math. Comput. 110 (2000), 251-264.

DOI: 10.1016/s0096-3003(99)00131-9

Google Scholar

[18] G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl. 135 (1988), 501-544.

Google Scholar