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A simple perturbation approach to Blasius equation. (English) Zbl 1028.65085
Summary: We couple the iteration method with the perturbation method to solve the well-known Blasius equation. The obtained approximate analytic solutions are valid for the whole solution domain. Comparison with {\it L. Howarth}’s numerical solution [On the solution of the laminar boundary layer equation, Proc. R. Soc. Lond. A 164, 547-579 (1938)] reveals that the proposed method is of high accuracy, the first iteration step leads to 6.8% accuracy, and the second iteration step yields the 0.73% accuracy of initial slop.

65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
34B40Boundary value problems for ODE on infinite intervals
34B30Special ODE (Mathieu, Hill, Bessel, etc.)
Full Text: DOI
[1] He, J. H.: Approximate analytical solution of Blasius’s equation. Commun. nonlinear sci. Numer. simulation 3, No. 4, 206-263 (1998)
[2] He, J. H.: Variational iteration method: a kind of nonlinear analytical technique: some examples. Int. J. Nonlinear mech. 34, No. 4, 699-708 (1999) · Zbl 05137891
[3] He, J. H.: Homotopy perturbation technique. Comput. meth. Appl. mech. Eng. 178, 257-262 (1999) · Zbl 0956.70017
[4] He, J. H.: A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int. J. Nonlinear mech. 35, 37-43 (2000) · Zbl 1068.74618
[5] He, J. H.: A review on some new recently developed nonlinear analytical techniques. Int. J. Nonlinear sci. Numer. simulation 1, No. 1, 51-70 (2000) · Zbl 0966.65056
[6] J.H. He, Iteration perturbation method for strongly nonlinear oscillations, J. Vib. Control, accepted for publication · Zbl 1015.70019
[7] Howarth, L.: On the solution of the laminar boundary layer equation. Proc. R soc. Lond. A 164, 547-579 (1938) · Zbl 64.1452.01
[8] Liao, S. J.: An approximate solution technique not depending on small parameters: a special example. Int. J. Nonlinear mech. 30, No. 3, 371-380 (1995) · Zbl 0837.76073
[9] Liao, S. J.: A uniformly valid analytic solution of 2-D viscous flow over a semi-infinite flat plate. J. fluid. Mech. 385, 101-128 (1999) · Zbl 0931.76017
[10] Nayfeh, A. H.: Introduction to perturbation techniques. (1981) · Zbl 0449.34001