Solution of the Falkner-Skan equation for wedge by Adomian decomposition method. (English) Zbl 1221.76136

Alizadeh, Ebrahim; Farhadi, Mousa; Sedighi, Kurosh; Ebrahimi-Kebria, H. R.; Ghafourian, Akbar

Commun. Nonlinear Sci. Numer. Simul. 14, No. 3, 724-733 (2009).

Summary: The Adomian Decomposition Method is employed in the solution of the two dimensional laminar boundary layer of Falkner–Skan equation for wedge. This work aims at the solution of momentum equation in the case of accelerated flow and decelerated flow with separation. The Adomian Decomposition Method provides an analytical solution in the form of an infinite power series. The effect of Adomian polynomials terms is considered on accuracy of the results. The velocity profiles in the boundary layer are obtained.

MSC:

76M25

Other numerical methods (fluid mechanics) (MSC2010)

Keywords:

Adomian decomposition method; nonlinear differential equations

References:

[1]	Hartree, D. H., On an equation occurring in Falkner and Skan’s approximate treatment of the equations of the boundary layer, Proc Cambr Philos Soc, 33, Part II, 223-239 (1937) · JFM 63.0432.03
[2]	Adomian, G., Solving Frontier problems of physics: the decomposition method (1994), Kluwer Academic Publication · Zbl 0802.65122
[3]	Adomian, G., A review of the decomposition method in applied mathematics, J Math Anal Appl, 135, 501-544 (1988) · Zbl 0671.34053
[4]	Wazwaz, A. M., The numerical solution of sixth-order boundary value problems by the modified decomposition method, Appl Math Comput, 118, 311-325 (2001) · Zbl 1023.65074
[5]	Jafari, H.; Daftardar-Gejji, V., Revised Adomian Decomposition Method for solving a system of non-linear equations, Appl Math Comput, 175, 1-7 (2006) · Zbl 1088.65047
[6]	Luo, X. G.; Wu, Q. B.; Zhang, B. Q., Revisit on partial solutions in the Adomian decomposition method: solving heat and wave equations, J Math Anal Appl, 321, 1, 353-363 (2006) · Zbl 1103.65106
[7]	Luo, X. G., A two-step Adomian Decomposition Method, Appl Math Comput, 170, 570-583 (2005) · Zbl 1082.65581
[8]	Zhang, X., A modification of the Adomian Decomposition Method for a class of nonlinear singular boundary value problems, J Comput Appl Math, 180, 377-389 (2005) · Zbl 1070.65067
[9]	Zhu, Y.; Chang, Q.; Wu, S., A new algorithm for calculating Adomian polynomials, Appl Math Comput, 169, 402-416 (2005) · Zbl 1087.65528
[10]	Abbasbandy, S., Extended Newton’s method for a system of non-linear equations by modified Adomian Decomposition Method, Appl Math Comput, 170, 648-656 (2005) · Zbl 1082.65531
[11]	Biazar, J.; Babolian, E.; Islam, R., Solution of ordinary differential equations by Adomian Decomposition Method, Appl Math Comput, 147, 3, 713-719 (2004) · Zbl 1034.65053
[12]	Daftardar-Gejji, V.; Jafari, H., An iterative method for solving nonlinear functional equations, J Math Anal Appl, 316, 753-763 (2006) · Zbl 1087.65055
[13]	Allan, F. M.; Al-Khaled, K., An approximation of the analytic solution of the shock wave equation, J Comput Appl Math, 192, 301-309 (2006) · Zbl 1091.65104
[14]	Pamuk, S., Solution of the porous media equation by Adomian’s decomposition method, Phys Lett A, 344, 184-188 (2005) · Zbl 1194.65148
[15]	Allan, F. M.; Syam, M. I., On the analytic solutions of the nonhomogeneous Blasius problem, J Comput Appl Math, 182, 362-371 (2005) · Zbl 1071.65108
[16]	Wang, L., A new algorithm for solving classical Blasius equation, Appl Math Comput, 157, 1-9 (2004) · Zbl 1108.65085
[17]	Hashim, I., Comments on a new algorithm for solving classical Blasius equation by L. Wang, J Comput Appl Math, 176, 700-703 (2006) · Zbl 1331.65103
[18]	Arslanturk, C., A decomposition method for fins efficiency of convective straight fins with temperature-dependent thermal conductivity, Int Commun Heat Mass Transfer, 32, 831-841 (2005)
[19]	Chang, M. H., A decomposition solution for fins with temperature dependent surface heat flux, Int J Heat Mass Transfer, 48, 1819-1824 (2005) · Zbl 1189.76519
[20]	Chiu, C. H.; Chen, C. K., A decomposition method for solving the convective longitudinal fins with variable thermal conductivity, Int J Heat Mass Transfer, 45, 2067-2075 (2002) · Zbl 1011.80011
[21]	Schilichting, H., Boundary-layer theory (2004), McGraw-Hill, Inc.