Abstract
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 language | English |
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Pages (from-to) | C57-C68 |
Number of pages | 12 |
Journal | The ANZIAM Journal |
Volume | 58 |
DOIs | |
Publication status | Published - 10 Oct 2017 |