zbMATH — the first resource for mathematics

Chebyshev finite difference method for the solution of boundary-layer equations. (English) Zbl 1059.76043
Summary: A Chebyshev finite difference method is proposed for solving the governing equations of boundary-layer flow. The Falkner-Skan equation has been solved as a model problem. We also solve the more general problem of the equations governing magnetohydrodynamic three-dimensional free convection on a vertical stretching surface. The comparisons between the data resulting from the present method and those obtained by others are made. The results indicate that the suggested method yields more accurate results than those computed by others.

76M20 Finite difference methods applied to problems in fluid mechanics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76W05 Magnetohydrodynamics and electrohydrodynamics
76R10 Free convection
Full Text: DOI
[1] Beckett, P.M., Finite difference solution of boundary layer type equation, Int. J. comput. math, 14, 183-190, (1983) · Zbl 0518.76031
[2] Blottner, F.G., Finite difference method of solution of the boundary-layer equations, Aiaa j, 8, 193-205, (1970) · Zbl 0223.76026
[3] Canuto, C.; Hussaini, M.Y.; Quarterini, A.; Zang, T.A., Spectral methods in fluid dynamics, (1988), Springer-Verlag Berlin
[4] Chamkha, A.J., Hydromagnetic three-dimensional free convection on a vertical stretching surface with heat generation or absorption, Int. J. heat fluid flow, 20, 84-92, (1999)
[5] Clenshaw, C.W.; Curtis, A.R., A method for numerical integration on an automatic computer, Numer. math, 2, 197-205, (1960) · Zbl 0093.14006
[6] Elbarbary, E.M.E.; El-Kady, M., Chebyshev finite difference approximation for the boundary value problems, Appl. math. comput, 139, 513-523, (2003) · Zbl 1027.65098
[7] El-Gendi, S.E., Chebyshev solution of differential, integral, and integro-differential equations, Comput. J, 12, 282-287, (1969) · Zbl 0198.50201
[8] El-Gindy, T.M.; El-Hawary, H.M.; Hussien, H.S., An optimization technique for the falkner – skan equation, J. optim, 35, 357-366, (1995) · Zbl 0926.76091
[9] El-Hawary, H.M., A deficient spline function approximation for boundary layer flow, Int. J. numer. meth. heat fluid flow, 11, 227-236, (2001) · Zbl 1012.76069
[10] Fox, L.; Parker, I.B., Chebyshev polynomials in numerical analysis, (1968), Clarendon Press Oxford · Zbl 0153.17502
[11] Gorla, R.S.R.; Sidawi, I., Free convection on a vertical stretching surface with suction and blowing, Appl. sci. res, 52, 247-257, (1994) · Zbl 0800.76421
[12] Gottlieb, D.; Orszag, S.A., Numerical analysis of spectral methods: theory and applications, CBMS-NSF regional conference series in applied mathematics, vol. 26, (1977), SIAM Philadelphia, PA · Zbl 0412.65058
[13] Nasr, H.; Hassanien, I.A.; El-Hawary, H.M., Chebyshev solution of laminar boundary layer flow, Int. J. comput. math, 33, 127-132, (1990) · Zbl 0756.76058
[14] Rosenhead, L., Laminar boundary layers, (1963), Oxford University Press Oxford · Zbl 0115.20705
[15] Voigt, R.G.; Gottlieb, D.; Hussaini, M.Y., Spectral methods for partial differential equations, (1984), SIAM Philadelphia, PA
[16] Wadia, A.R.; Payne, F.R., A boundary value technique for the analysis of laminar boundary layer flows, Int. J. comput. math, 9, 163-172, (1981) · Zbl 0454.76062
[17] White, F.M., Viscous fluid flow, (1974), McGraw-Hill New York · Zbl 0356.76003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.