Numerical solution to the Falkner-Skan equation: a novel numerical approach through the new rational a-polynomials

doi:10.1007/s10483-021-2777-5

摘要/Abstract

摘要： The new rational a-polynomials are used to solve the Falkner-Skan equation. These polynomials are equipped with an auxiliary parameter. The approximated solution to the Falkner-Skan equation is obtained by the new rational a-polynomials with unknown coefficients. To find the unknown coefficients and the auxiliary parameter contained in the polynomials, the collocation method with Chebyshev-Gauss points is used. The numerical examples show the efficiency of this method.

关键词: Falkner-Skan equation, rational Chebyshev polynomial, mapping parameter, collocation method, singular Sturm-Liouville problem

Abstract: The new rational a-polynomials are used to solve the Falkner-Skan equation. These polynomials are equipped with an auxiliary parameter. The approximated solution to the Falkner-Skan equation is obtained by the new rational a-polynomials with unknown coefficients. To find the unknown coefficients and the auxiliary parameter contained in the polynomials, the collocation method with Chebyshev-Gauss points is used. The numerical examples show the efficiency of this method.

Key words: Falkner-Skan equation, rational Chebyshev polynomial, mapping parameter, collocation method, singular Sturm-Liouville problem

中图分类号:

S. ABBASBANDY, J. HAJISHAFIEIHA. Numerical solution to the Falkner-Skan equation: a novel numerical approach through the new rational a-polynomials[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(10): 1449-1460.

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