Abstract
Three spectral collocation methods, namely Laguerre collocation (LC), Laguerre Gauss Radau collocation (LGRC) and mapped Chebyshev collocation (ChC) are used in order to solve some challenging systems of boundary layer problems of third and second orders. The last two methods enable a Fourier type analysis, mainly (fast) polynomial transformations, which can be used in order to improve the process of optimization of the scaling parameters. Generally, the second method mentioned above produces the best results. Unfortunately they remain sub geometric with respect to the accuracy. However, all methods avoid domain truncation and rather arbitrary shooting techniques. Some challenging problems from fluid mechanics, including non-newtonian fluids are accurately solved.
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Gheorghiu, CI. Spectral collocation solutions to systems of boundary layer type. Numer Algor 73, 1–14 (2016). https://doi.org/10.1007/s11075-015-0083-6
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DOI: https://doi.org/10.1007/s11075-015-0083-6