A numerical method for solving two forms of Blasius equation is proposed. The Blasius equation is a third order nonlinear ordinary differential equation, which arises in the problem of the two-dimensional laminar viscous flow over a half-infinite domain. The approach is based on differential transform method and Padé approximations. In this scheme, the solution takes the form of a convergent series with easily computable components. The obtained series solution is combined with the diagonal Padé approximations to handle the boundary condition at infinity for only one of these forms. The numerical results demonstrates the validity and applicabilty of the method and a comparison is made with existing results.
BelhachmiZ.BrightB. and TaousK.On the concave solutions of the Blasius equations, Acta Mathematica Universitatis Comenianae, 2000, LXIX2, 199–214.
2.
DattaB. K., Analytic solution for the Blasius equation, Indian Journal of Pure and Applied Mathematics, 2003, 34 (2), 237–240.
3.
ZhouJ. K., Differential Transformation and Its Applications for Electrical Circuits, 1986, Huazhong University Press, Wuhan.
4.
WazwazA. M., Analytical approximations and Padé approximants for Volterra's population model, Applied Mathematics and Computation, 1999, 100, 13–25.
5.
WazwazA. M., A study on aboundary-layer equation arising in an incompressible fluid, Applied Mathematics and Computation, 1997, 87, 199–204.
6.
WazwazA. M.PartialDifferential Equations: Methods and Applications, 2002, Balkema, The Netherlands.
7.
BoydJ., Padé approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain, Journal Computational Physics, 1997, 11 (3) 299–303.
8.
BakerG.A., Essentials of Padé approximants, 1975, Academic Press, London.
9.
ArikoğluA. and ÖzkolI., Solution of boundary value problems for integro-differential equations by using differential transform method, Applied Mathematics and Computation, 2005, 168, 1145–1158.
10.
AyazF.Solutions of the system of differential equations by differential transform method, Applied Mathematics and Computation, 2004, 147, 547–567.
11.
LiuH.SongY., Differential transform method applied to high index differential-algebraic equations, Applied Mathematics and Computation, 2007, 184, 748–753.
12.
HassanI. H. A. H., Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems, Chaos, Solitons and Fractals, 2008, 36, 53–65.
13.
BildikN.KonuralpA.BekF. and KüçükarslanS., Solution of different type of the partial differential equation by differential transform method and Adomian decomposition method, Applied Mathematics and Computation, 2006, 172, 551–567.
14.
ErtürkV.S. and MomaniS., Comparing numerical methods for solving fourth-order boundary value problems, Applied Mathematics and Computation, 2007, 188, 1963–1968.
15.
WazwazA. M., The variational iteration method for solving two forms of Blasius equation on a half-infinite domain, Applied Mathematics and Computation, 2007, 188, 485–491.
16.
ChenC. K. and HoS. H., Solving partial differential equations by two-dimensional differential transform method, Applied Mathematics and Computation, 1999, 106, 171–179.
17.
HassanI. H. A. H., Differential transformation technique for solving higher-order initial value problems, Applied Mathematics and Computation, 2004, 154, 299–311.
18.
JangM. J.ChenC. L. and LiyY. C., On solving the initial-value problems using the differential transformation method, Applied Mathematics and Computation, 2000, 115, 145–160.
19.
JangM. J.ChenC. L. and LiyY. C., Two-dimensional differential transform for partial differential equations, Applied Mathematics and Computation, 2001, 21, 261–270.
20.
SchlichtingH., Boundary Layer Theory, 1968, McGraw Hill, NY.
21.
BakerG.A., Essentials of Padé approximants, Academic Press, London, 1975.
