Numerical Solution of Blasius Equation through Neural Networks Algorithm

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References

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[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