A Modified Laplace Decomposition Algorithm Solution for Blasius’ Boundary Layer Equation of the Flat Plate in a Uniform Stream
In this work, we apply the Modified Laplace
decomposition algorithm in finding a numerical solution of Blasius’
boundary layer equation for the flat plate in a uniform stream. The
series solution is found by first applying the Laplace transform to the
differential equation and then decomposing the nonlinear term by the
use of Adomian polynomials. The resulting series, which is exactly the
same as that obtained by Weyl 1942a, was expressed as a rational
function by the use of diagonal padé approximant.
<p>[1] G. Adomian, “A review of the decomposition method and some recent
results for nonlinear equation”, Math. Comput. Modeling, 13(7) (1990),
17-43.
[2] G. Adomian, “Solving Frontier Problems of Physics: The Decomposition
Method”, vol. 60 of Fundamental Theories of Physics, Kluwer Academic,
Dordrecht, 1994.
[3] . Yahaya Qaid Hassan, Liu Ming Zhu. “A note on the use of modified
Adomian decomposition method for solving singular boundary value
problems of higher-order ordinary differential equations”,
Communications in Nonlinear Science and Numerical Simulation, 2009,
14(8), 3261-3265.
[4] Yahaya Qaid Hassan, Liu Ming Zhu, “Solving singular boundary value
problems of higher-order ordinary differential equations by modified
Adomian decomposition method”, Communications in Nonlinear Science
and Numerical Simulation, 2009, 14(6), 2592-2596.
[5] S. N. Venkatarangan, T. R Sivakumar，“A modification of Adomian’s
decomposition method for boundary value problems with homogenous
boundary conditions”， Jour. Math. Phys. Sci.，1990, 24, 19-25.
[6] A. M. Wazwaz. “Pade approximants and Adomian decomposition method
for solving the Flierl-Petviasihvili equation and its variants”, Appl. Math.
Comput. 2006, 182: 1812-1818.
[7] Khuri S. A., “A Laplace decomposition algorithm applied to a class of
nonlinear differential equations”, J. Appl. Math., 2001, 1(4), 141-155.
[8] Yusufoglu (Agadjanov) E., “Numerical Solution of Duffing Equation by
the Laplace decomposition algorithm”, Applied Mathematics and
Computation, 2006, 177, 572-580.
[9] Yasir Khan, “An effective modification of the Laplace decomposition
method for nonlinear equations”, Int. J. Nonlin. Sci. Num. Simul., 2009,
10(11-12), 1373- 1376.
[10] Yasir Khan, Naeem Faraz. “Application of modified Laplace
decomposition method for solving boundary layer equation”, Journal of
King Saud University (Science), 2011, 23, 115-119.
[11] Rashidi, M. M. “The modified differential transforms method for solving
MHD boundary-Layer equations”, Comput. Phys. Commun., 2009, 180,
2210-2217.
[12] L. Rosenhead. “Laminar Boundary Layers”, Oxford University Press,
1963, pp 222-236.</p>
<p>[1] G. Adomian, “A review of the decomposition method and some recent
results for nonlinear equation”, Math. Comput. Modeling, 13(7) (1990),
17-43.
[2] G. Adomian, “Solving Frontier Problems of Physics: The Decomposition
Method”, vol. 60 of Fundamental Theories of Physics, Kluwer Academic,
Dordrecht, 1994.
[3] . Yahaya Qaid Hassan, Liu Ming Zhu. “A note on the use of modified
Adomian decomposition method for solving singular boundary value
problems of higher-order ordinary differential equations”,
Communications in Nonlinear Science and Numerical Simulation, 2009,
14(8), 3261-3265.
[4] Yahaya Qaid Hassan, Liu Ming Zhu, “Solving singular boundary value
problems of higher-order ordinary differential equations by modified
Adomian decomposition method”, Communications in Nonlinear Science
and Numerical Simulation, 2009, 14(6), 2592-2596.
[5] S. N. Venkatarangan, T. R Sivakumar，“A modification of Adomian’s
decomposition method for boundary value problems with homogenous
boundary conditions”， Jour. Math. Phys. Sci.，1990, 24, 19-25.
[6] A. M. Wazwaz. “Pade approximants and Adomian decomposition method
for solving the Flierl-Petviasihvili equation and its variants”, Appl. Math.
Comput. 2006, 182: 1812-1818.
[7] Khuri S. A., “A Laplace decomposition algorithm applied to a class of
nonlinear differential equations”, J. Appl. Math., 2001, 1(4), 141-155.
[8] Yusufoglu (Agadjanov) E., “Numerical Solution of Duffing Equation by
the Laplace decomposition algorithm”, Applied Mathematics and
Computation, 2006, 177, 572-580.
[9] Yasir Khan, “An effective modification of the Laplace decomposition
method for nonlinear equations”, Int. J. Nonlin. Sci. Num. Simul., 2009,
10(11-12), 1373- 1376.
[10] Yasir Khan, Naeem Faraz. “Application of modified Laplace
decomposition method for solving boundary layer equation”, Journal of
King Saud University (Science), 2011, 23, 115-119.
[11] Rashidi, M. M. “The modified differential transforms method for solving
MHD boundary-Layer equations”, Comput. Phys. Commun., 2009, 180,
2210-2217.
[12] L. Rosenhead. “Laminar Boundary Layers”, Oxford University Press,
1963, pp 222-236.</p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56331", author = "M. A. Koroma and Z. Chuangyi and A. F. and Kamara and A. M. H. Conteh", title = "A Modified Laplace Decomposition Algorithm Solution for Blasius’ Boundary Layer Equation of the Flat Plate in a Uniform Stream", abstract = "In this work, we apply the Modified Laplace
decomposition algorithm in finding a numerical solution of Blasius’
boundary layer equation for the flat plate in a uniform stream. The
series solution is found by first applying the Laplace transform to the
differential equation and then decomposing the nonlinear term by the
use of Adomian polynomials. The resulting series, which is exactly the
same as that obtained by Weyl 1942a, was expressed as a rational
function by the use of diagonal padé approximant.
", keywords = "Modified Laplace decomposition algorithm, Boundary
layer equation, Padé approximant, Numerical solution.", volume = "7", number = "7", pages = "1152-5", }
