The Mathematical Institute, University of Oxford, Eprints Archive

A fast and well-conditioned spectral method

Olver, Sheehan and Townsend, Alex (2012) A fast and well-conditioned spectral method. Technical Report. SIAM Review. (Submitted)

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Abstract

A novel spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes $O(m^{2}n)$ operations, where $m$ is the number of Chebyshev points needed to resolve the coefficients of the differential operator and $n$ is the number of Chebyshev points needed to resolve the solution to the differential equation. We prove stability of the method by relating it to a diagonally preconditioned system which has a bounded condition number, in a suitable norm. For Dirichlet boundary conditions, this reduces to stability in the standard 2-norm.

Item Type:Technical Report (Technical Report)
Subjects:O - Z > Special functions
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1464
Deposited By:Lotti Ekert
Deposited On:16 Feb 2012 08:11
Last Modified:16 Feb 2012 08:11

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