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Numerical Solution of Blasius Equation through Neural Networks Algorithm

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DOI: 10.4236/ajcm.2014.43019    5,449 Downloads   7,391 Views   Citations

ABSTRACT

In this paper mathematical techniques have been used for the solution of Blasius differential equation. The method uses optimized artificial neural networks approximation with Sequential Quadratic Programming algorithm and hybrid AST-INP techniques. Numerical treatment of this problem reported in the literature is based on Shooting and Finite Differences Method, while our mathematical approach is very simple. Numerical testing showed that solutions obtained by using the proposed methods are better in accuracy than those reported in literature. Statistical analysis provided the convergence of the proposed model.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Ahmad, I. and Bilal, M. (2014) Numerical Solution of Blasius Equation through Neural Networks Algorithm. American Journal of Computational Mathematics, 4, 223-232. doi: 10.4236/ajcm.2014.43019.

References

[1] Howarth, L. (1938) On the Solution of the Laminar Boundary Layer Equations. Proceedings of the London Mathematical Society, 164, 547-579. http://dx.doi.org/10.1098/rspa.1938.0037
[2] Liao, S.J. (1999) An Explicit, Totally Analytic Approximate Solution for Blasius Viscous Flow Problems. International Journal of Non-Linear Mechanics, 34, 759-778.
http://dx.doi.org/10.1016/S0020-7462(98)00056-0
[3] Liao, S.J. (1992) The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems. Ph.D. Thesis, Shanghai Jiao Tong University, Shanghai.
[4] Shishkin, G.I. (2001) Grid Approximation of the Solution to the Blasius Equation and of its Derivatives. Computational Mathematics and Mathematical Physics, 41, 37-54.
[5] Yu, L.T. and Kuang, C.C. (1998) The Solution of the Blasius Equation by the Differential Transformation Method. Mathematical and Computer Modeling, 28, 101-111.
[6] Schlichting, H. (1979) Boundary Layer Theory. McGraw-Hill, New York, 127-144.
[7] Coppel, W.A. (1960) On a Differential Equation of Boundary Layer Theory. Philosophical Transactions of the Royal Society A, 253, 101-136.
[8] Allan, F.M. and Abu-Saris, R.M. (1999) On the Existence and Non-Uniqueness of Nonhomogeneous Blasius Problem. Proceedings of the Second Pal. International Conference, Gorden and Breach, Newark.
[9] Howarth, L. (1938) On the Solution of the Laminar Boundary Layer Equations. Proceedings of the London Mathematical Society, 164, 547-579. http://dx.doi.org/10.1098/rspa.1938.0037
[10] Liao, S.J. (1999) An Explicit, Totally Analytic Approximate Solution for Blasius Viscous Flow Problems. International Journal of Non-Linear Mechanics, 34, 759-778.
http://dx.doi.org/10.1016/S0020-7462(98)00056-0
[11] Khan, J.A. and Zahoor Raja, M.A. (2013) Artificial Intelligence based Solver for Governing Model of Radioactivity Cooling, Self-Gravitating Clouds and Clusters of Galaxies. Research Journal of Applied Sciences, Engineering and Technology, 6, 450-456.
[12] Zahoor Raja, M.A., Khan, J.A. and Qureshi, I.M. (2010) A New Stochastic Approach for Solution of Riccati Differential Equation of Fractional Order. Annals of Mathematics and Artificial Intelligence, 60, 229-250.
http://dx.doi.org/10.1007/s10472-010-9222-x
[13] Zahoor Raja, M.A. and Samar, R. (2014) Numerical Treatment for Nonlinear MHD Jeffery-Hamel Problem Using Neural Networks Optimized with Interior Point Algorithm. Neurocomputing, 124, 178-193.
http://dx.doi.org/10.1016/j.neucom.2013.07.013

  
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