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Conformal Maps to Multiply-Slit Domains and Applications

Abstract:

By exploiting conformal maps to vertically slit regions in the complex plane, a recently developed rational spectral method [Tee and Trefethen, 2006] is able to solve PDEs with interior layer-like behaviour using significantly fewer collocation points than traditional spectral methods. The conformal maps are chosen to 'enlarge the region of analyticity' in the solution: an idea which can be extended to other numerical methods based upon global polynomial interpolation. Here we show how such m...

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Publication date:
2008-10-05
URN:
uuid:3e41d008-6441-4252-99c0-2bfd7431faa3
Local pid:
oai:eprints.maths.ox.ac.uk:1062

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