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

Andrew Cullen, Simon Clarke

Research output: Contribution to journalArticleResearchpeer-review


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.
Original languageEnglish
Pages (from-to)C57-C68
Number of pages12
JournalThe ANZIAM Journal
Publication statusPublished - 10 Oct 2017

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