Chebyshev spectral collocation in space and time for the heat equation

Autor:	S. H. Lui, Sarah Nataj
Rok vydání:	2020
Předmět:	Collocation Elliptic partial differential equation Finite difference Applied mathematics Heat equation Spectral method Chebyshev filter Condition number Legendre polynomials Analysis Mathematics
Zdroj:	ETNA - Electronic Transactions on Numerical Analysis. 52:295-319
ISSN:	1068-9613
DOI:	10.1553/etna_vol52s295
Popis:	Spectral methods can solve elliptic partial differential equations (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 the spatial derivatives. This mismatch destroys the spectral convergence of the numerical solution. Spectral methods that converge spectrally in both space and time have appeared recently. This paper shows that a Chebyshev spectral collocation method of Tang and Xu for the heat equation converges exponentially when the solution is analytic. We also derive a condition number estimate of the global spectral operator. Another space-time Chebyshev collocation scheme that is easier to implement is proposed and analyzed. This paper is a continuation of the first author's earlier paper in which two Legendre space-time collocation methods were analyzed.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e3d5b2f32e1a1e8379936bd85933817d https://doi.org/10.1553/etna_vol52s295 Zobrazit plný text záznamu