A fast, spectrally accurate solver for the Falkner--Skan equation

Andrew Craig Cullen, Simon Clarke


We present a new numerical technique, the Gegenbauer homotopy analysis method, which allows for the construction of iterative solutions to nonlinear differential equations. This technique is a numerical extension of the semi-analytic homotopy analysis method that exhibits spectral convergence while performing sparse matrix operations in Gegenbauer space. This technique is used to present solutions to the Falkner--Skan equation, a well known problem in boundary layer fluid dynamics. These solutions are compared to previously published works, and the convergence properties exhibited by this new technique are considered.

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nonlinear; numerical methods; differential equation; boundary value problem; Falkner-Skan; Blasius;

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DOI: http://dx.doi.org/10.21914/anziamj.v58i0.11746

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