The Mathematical Institute, University of Oxford, Eprints Archive

A rational spectral collocation method with adaptively transformed Chebyshev grid points

Tee, T. W. and Trefethen, Lloyd N. (2005) A rational spectral collocation method with adaptively transformed Chebyshev grid points. Technical Report. Unspecified. (Submitted)

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Abstract

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are approximated by the locations of poles of Chebyshev-Padé approximants. Numerical experiments on two time-dependent problems, one with finite time blow-up and one with a moving front, indicate that the method far outperforms the standard Chebyshev spectral collocation method for problems whose solutions have singularities in the complex plan close to [-1,1].

Item Type:Technical Report (Technical Report)
Subjects:A - C > Approximations and expansions
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1131
Deposited By:Lotti Ekert
Deposited On:12 May 2011 08:36
Last Modified:12 May 2011 08:36

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