BIRS Workshop Lecture Videos
Space-time Legendre Spectral Collocation Methods Lui, Shaun
Spectral methods solve elliptic PDEs numerically with errors bounded by an exponentially decaying function of the number of modes when the solution is analytic. For time dependent problems, almost all focus has been on low-order finite difference schemes for the time derivative and spectral schemes for spatial derivatives. Spectral methods which converge spectrally in both space and time have appeared recently. This paper shows the exponential convergence of the heat equation for a Legendre spectral collocation method. A condition number estimate of the method is also given.
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