2995-3162ISSN (Online)
Volume 1 , Issue 2 , PP: 20-31, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
Arwa Hajjari 1 *
Doi: https://doi.org/10.54216/PMTCS.010203
This paper presents an iterative method based on spline function approximations for the numerical solution of the Falkner–Skan equation (FSE) over a semi-infinite interval. This technique will transform the FSE into two initial value problems, so the solution of FSE will be reduced from the interval [0,¥[ into [0,1]. Spline approximations are applied directly to the FSE without its reducing into a system of first-order differential equations, thus, the algorithm of spline method has a computational cost that is cost-effective. The spline solution of the FSE is existent and unique, and the convergence analysis for the spline method applied to the FSE is discussed. Numerical results are compared with those obtained by previous methods under various instances of the FSE. The comparisons show the accuracy and efficiency of the presented methodology.
Numerical approximation , differential equation , Falkner-Skan equation
[1] ASAITHAMBI, A. Numerical solution of the Falkner–Skan equation using piecewise linear functions. Appl. Math. and Comput. 159, 2004, 267-273.
[2] BECKETT, P. M. Finite difference solutions of boundary-layer type equations, Intern. J. Computer Math., Vol. 14, 1983, 183-190.
[3] ELBARBARY, E.M.E. Chebyshev finite difference method for the solution of boundary-layer equations, Appl. Math. and Comput. 160, 2005, 487–498.
[4] EL-GINDY, T. M.; EL HAWARY, H. M.; HUSSIEN, H. S. An optimization technique for the falkner-skan equation, Optimization, 1995, Vol. 35, 357-366.
[5] EL-HAWARY, H.M. A deficient spline function approximation for boundary layer flow, Int. J. Numer. Meth. Heat Fluid Flow, 11, 2001, 227–236.
[6] KUDENATTI, R. B.; AWATI, V. B. Solution of pressure gradient stretching plate with suction, Appl. Math. and Comput., 210, 2009, 151–157.
[7] KUO, B. L. Heat transfer analysis for the Falkner–Skan wedge flow by the differential transformation method, International Journal of Heat and Mass Transfer, 48, 2005, 5036–5046.
[8] NASR, H.; HASSANIEN, I. A.; EL-HAWARY, H. M. Chebyshev solution of laminar boundary layer flow. Intern. J. Computer Math, vol 33, 1990, 127-132.
[9] PARAND, K.; TAGHAVI, A. Rational scaled generalized Laguerre function collocation method for solving the Blasius equation, Journal of Comput. and appl. Math., 233, 2009, 980-989.
[10] PARAND, K.; SHAHINI, M.; DEHGHAN, M. Solution of a laminar boundary layer flow via a numerical method. Commun Nonlinear Sci Numer Simulat, 15, 2010, 360–367.
[11] WADIA, A. R.; PAYNE, F. R. A boundary value technique for the analysis of laminar boundary layer flows. Intern. J. Computer Math, Section B, vol 9, 1981, 163-172.
[12] YAO, B. Approximate analytical solution to the Falkner–Skan wedge flow with the permeable wall of uniform suction. Commun Nonlinear Sci Numer Simulat. 14, 2009, 3320-3326.
[13] ZHANG, J.; CHEN, B. An iterative method for solving the Falkner Skan equation. Appl. Math. and Comput., 210, 2009, 215–222.
[14] ZHU, S.; WU, Q.; CHENG, X. Numerical solution of the Falkner Skan equation based on quasilinearization. Appl. Math. And Comput. 215, 2009, 2472–2485.
