×

Numerical solution for the Falkner-Skan equation. (English) Zbl 1135.76039

Summary: An analysis is presented for numerical solution of Falkner-Skan equation. The nonlinear ordinary differential equation is solved using Adomian decomposition method (ADM). The condition at infinity is applied to the related Padé approximation. By using MATHEMATICA\(^{\text{TM}}\), we calculate the Adomian polynomials and Padé approximation of the obtained series solution. The solutions obtained by ADM and by the shooting method are in agreement with those obtained in previous works, and are efficient to use.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D10 Boundary-layer theory, separation and reattachment, higher-order effects

Software:

Mathematica
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adomian, G., Nonlinear stochastic systems theory and applications to physics (1989), Kluwer, Academic · Zbl 0659.93003
[2] Adomian, G., A review of the decomposition method and some recent results for nonlinear equations, Comput Math Appl, 21, 101-127 (1991) · Zbl 0732.35003
[3] Adomian, G.; Rach, R. C.; Meyers, R. E., An efficient methodology for the physical sciences, Kybenetes, 20, 24-34 (1991) · Zbl 0744.65039
[4] Adomian, G., Solution of physical problems by decomposition, Comput Math Appl, 27, 145-154 (1994) · Zbl 0803.35020
[5] Adomian, G., Solving frontier problems of physics : The decomposition method (1994), Kluwer: Kluwer Boston · Zbl 0802.65122
[6] Asaithambi, N. S., A numerical method for the solution of the Falkner-Skan equation, Appl Math Comput, 81, 259-264 (1997) · Zbl 0873.76049
[7] Asaithambi, N. S., A finite-difference method for the solution of the Falkner-Skan equation, Appl Math Comput, 92, 135-141 (1998) · Zbl 0973.76581
[8] Asaithambi, N. S., A second-order finite-difference method for the Falkner-Skan equation, Appl Math Comput, 156, 3, 779-786 (2004) · Zbl 1108.76048
[9] Asaithambi, N. S., Numerical solution of the Falkner-Skan equation using piecewise linear functions, Appl Math Comput, 159, 1, 267-273 (2004) · Zbl 1098.65110
[10] Baker, G. A.; Graves-Morris, P., Padé approximates. Part I: Basic theory (1981), Addison-Wesley · Zbl 0603.30044
[11] Biazar, J.; Babolian, E.; Kember, G.; Nouri, A.; Isla, R., An alternate algorithm for computing Adomian polynomials in special cases, Appl Math Comput, 138, 523-529 (2003) · Zbl 1027.65076
[12] Cebeci, T.; Keller, H. B., Shooting and parallel shooting methods for solving the Falkner-Skan boundary-layer equation, J Comput Phys, 7, 289-300 (1971) · Zbl 0215.58201
[13] Kaya, Dogˇan; Yokus, Asif, A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations, Math Comput Simul, 60, 507-512 (2002) · Zbl 1007.65078
[14] Kaya, Dogˇan; El-Sayed, S. M., An application of the decomposition method for the generalized KdV and RLW equations, Chaos, Solitons & Fractals, 17, 5, 869-877 (2003) · Zbl 1030.35139
[15] El-Danaf, T. S.; Ramadan, M. A.; Abd Alaal, F. E.I., The use of Adomian decomposition method for solving the regularized long-wave equation, Chaos, Solitons & Fractals, 26, 3, 747-757 (2005) · Zbl 1073.35010
[16] El-Sayed, S. M., The decomposition method for studying the Klein-Gordon equation, Chaos, Solitons & Fractals, 18, 5, 1025-1030 (2003) · Zbl 1068.35069
[17] El-Sayed, S. M.; Abdel-Aziz, M. R., A comparison of Adomian decomposition method and wavelet-Galerkin method for solving integro-differential equations, Appl Math Comput, 136, 151-159 (2003) · Zbl 1023.65149
[18] Jiao, Y. C.; Yamamoto, Y.; Dang, C.; Hao, Y., An aftertreatment technique for improving the accuracy of Adomian decomposition method, Comput Math Appl, 43, 783-798 (2002) · Zbl 1005.34006
[19] Lesnic, D., Blow-up solutions obtained using the decomposition method, Chaos, Solitons & Fractals, 28, 3, 776-787 (2006) · Zbl 1109.35024
[20] Na, T. Y., Computational methods in engineering boundary value problems (1979), Academic Press: Academic Press New York · Zbl 0456.76002
[21] Sadefo Kamdem, J.; Zhijun, Qiao, Decomposition method for the Camassa-Holm equation, Chaos, Solitons & Fractals, 31, 2, 437-447 (2007) · Zbl 1138.35396
[22] Geng, Xianguo, Decomposition of a hierarchy of nonlinear evolution equations, Chaos, Solitons & Fractals, 16, 749-758 (2003) · Zbl 1030.37044
[23] Wazwaz, A. M.; El-Sayed, S. M., A new modification of the Adomian decomposition method for linear and nonlinear operators, Appl Math Comput, 122, 393-405 (2001) · Zbl 1027.35008
[24] Wazwaz, A. M., Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method, Chaos, Solitons & Fractals, 12, 12, 2283-2293 (2001) · Zbl 0992.35092
[25] Wazwaz, A. M., Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method, Chaos, Solitons & Fractals, 12, 8, 1549-1556 (2001) · Zbl 1022.35051
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.