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Modified Hermite polynomials in the spectral approximation for boundary layer problems

Published online by Cambridge University Press:  17 April 2009

Nevenka Adžić
Nevenka Adžić
Affiliation:
Faculty of Technical Sciences Institute for Appl. Fund. Disc. VeljkaVlahovića 3 21000 Novi SadYugoslavia
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Abstract

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The solution of the linear boundary layer problem is presented as a sum of the reduced solution and the layer function, which is approximated by a truncated orthogonal series. The layer subinterval is determined through the numerical layer length, which depends on the perturbation parameter and the degree of the spectral approximation. Modified Hermite polynomials are used as an orthogonal basis. Systematic methods are presented to obtain the recurrence relations for the coefficients in modified Hermite series solution of linear differential equations with polynomial coefficients. The upper bound for the error function is constructed and the numerical example is included.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 2 , April 1992 , pp. 267 - 276
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Doolan, E.P., Miller, J.J.H. and Schilders, W.H.A., Uniform numerical methods for problems with initial and boundary layers (Dublin Boole Press, 1980).Google Scholar
[2]Horner, T.S., ‘Recurrence relations for the coefficients in Chebyshev series solution of ordinary differential equations’, Math. Comp. 35 (1980), 893–905.CrossRefGoogle Scholar
[3]Chang, R.Y. and Wang, M.L., ‘The properties of modified Hermite polynomials and their applications to functional differential equations’, J. Chinese Inst. Engrs. 9 (1986), 75–81.CrossRefGoogle Scholar
[4]Adžić, N., ‘Recurrence relations for the coefficients in Legendre solution for some ordinary differential equations’, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 19 (1988), 14–25.Google Scholar
[5]Adžić, N.?, ‘On orthogonal series solution for boundary layer problems’, Publ. Inst. Math. Univ. Nancago 49 (63) (1990) (to appear).Google Scholar
[6]Lorenz, J., ‘Stability and monotonicity properties of stiff quasilinear boundary problems’, Univ. u. Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 12 (1982), 151–173.Google Scholar