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 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.


65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B40 Boundary value problems on infinite intervals for ordinary differential equations
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
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[1] He, J. H., Approximate analytical solution of Blasius’s equation, Commun. Nonlinear Sci. Numer. Simulation, 3, 4, 206-263 (1998)
[2] He, J. H., Variational iteration method: a kind of nonlinear analytical technique: some examples, Int. J. Nonlinear Mech., 34, 4, 699-708 (1999) · Zbl 1342.34005
[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, 1, 51-70 (2000) · Zbl 0966.65056
[7] Howarth, L., On the solution of the laminar boundary layer equation, Proc. R Soc. Lond. A, 164, 547-579 (1938) · JFM 64.1452.01
[8] Liao, S. J., An approximate solution technique not depending on small parameters: a special example, Int. J. Nonlinear Mech., 30, 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), John Wiley & Sons: John Wiley & Sons New York · Zbl 0449.34001
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