The solution of the Blasius equation by the differential transformation method. (English) Zbl 1076.34501

Yu, Lien-Tsai; Chen, Cha’o-Kuang

Math. Comput. Modelling 28, No. 1, 101-111 (1998).

Summary: The Blasius equation of boundary layer flow is a third-order nonlinear differential equation. We solved the equation using the differential transformation method. It yields not only the numerical values, but also power series closed-form solutions. The results prove that the differential transformation method is a powerful technique for nonlinear problems.

MSC:

34A25	Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
76D10	Boundary-layer theory, separation and reattachment, higher-order effects

Keywords:

Differential transformation method; Blasius equation; Nonlinear equation; Power series

References:

[1]	Schlichtung, H., Boundary Layer Theory, ((1979), McGraw-Hill: McGraw-Hill New York), 127-144
[2]	Özisik, M. N., Basic Heat Transfer, ((1977), McGraw-Hill: McGraw-Hill New York), 224-227
[3]	Na, T. Y., Computational Methods in Engineering Boundary Value Problems, ((1979), Academic Press: Academic Press New York), 137-148 · Zbl 0456.76002
[4]	Ames, W. F., Nonlinear Ordinary Differential Equations in Transport Processes, ((1968), Academic Press: Academic Press New York), 121-127
[5]	Zhou, X., Differential Transformation and Its Applications for Electrical Circuits (1986), Huazhong University Press: Huazhong University Press Wuhan, China, (in Chinese)