Spectral approximation of third-order problems
type: Item
instance of: scholarly article
title: Spectral approximation of third-order problems
zbMATH Open document ID: 0953.65072
DOI: 10.1023/A:1023221619567
author: Wilhelm Heinrichs
published in: Journal of Scientific Computing
publication date: 2001-01-10T00:00:00Z
review text: The author introduces a Chebyshev collocation method for the partial differential equation \(u_t = u_{xxx}\) on the set \((x, t) \in (-1, 1) \times (0, T]\). The boundary conditions are of a Dirichlet sort which ensure stability. A computational investigation suggests that collocation at the Gauss-Lobatto points produces a stable numerical method. The author also presents a finite-difference preconditioner to be used with implicit temporal discretizations.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K30
zbMATH DE Number: 1455177
zbMATH Keywords: Chebyshev collocation method
zbMATH Keywords: third-order problems
zbMATH Keywords: stability
zbMATH Keywords: finite-difference preconditioner
reviewed by: Gerald W. Hedstrom
MaRDI profile type: Publication
full work available at URL: a:1023221619567
OpenAlex ID: W85487640
description: scientific article; zbMATH DE number 1455177