The Chebyshev–Legendre Method: Implementing Legendre Methods on Chebyshev Points

Wai Sun Don; David Gottlieb

doi:10.1137/0731079

The Chebyshev–Legendre Method: Implementing Legendre Methods on Chebyshev Points

Wai Sun Don^*
, David Gottlieb

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

70 Citations (Scopus)

Abstract

A new collocation method for the numerical solution of partial differential equations is presented. This method uses the Chebyshev collocation points, but, because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular L₂ estimates can be easily obtained for hyperbolic and parabolic problems.

Original language	English
Pages (from-to)	1519-1534
Number of pages	16
Journal	SIAM Journal on Numerical Analysis
Volume	31
Issue number	6
DOIs	https://doi.org/10.1137/0731079
Publication status	Published - Dec 1994

User-Defined Keywords

Chebyshev-Legendre
penalty method
differentiation matrix
stability

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10.1137/0731079

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@article{c69809af86504026a66fb87784d4481c,

title = "The Chebyshev–Legendre Method: Implementing Legendre Methods on Chebyshev Points",

abstract = "A new collocation method for the numerical solution of partial differential equations is presented. This method uses the Chebyshev collocation points, but, because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular L2 estimates can be easily obtained for hyperbolic and parabolic problems.",

keywords = "Chebyshev-Legendre, penalty method, differentiation matrix, stability",

author = "Don, \{Wai Sun\} and David Gottlieb",

note = "Publisher Copyright: {\textcopyright} 1994 Society for Industrial and Applied Mathematics. Funding Information: This research was supported by Air Force Office of Scientific Research grant 93-1-0090, Defense Advanced Research Projects Agency grant N00014-91-J-4016, and National Science Foundation grant DMS-92-11820.",

year = "1994",

month = dec,

doi = "10.1137/0731079",

language = "English",

volume = "31",

pages = "1519--1534",

journal = "SIAM Journal on Numerical Analysis",

issn = "0036-1429",

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TY - JOUR

T1 - The Chebyshev–Legendre Method

T2 - Implementing Legendre Methods on Chebyshev Points

AU - Don, Wai Sun

AU - Gottlieb, David

N1 - Publisher Copyright: © 1994 Society for Industrial and Applied Mathematics. Funding Information: This research was supported by Air Force Office of Scientific Research grant 93-1-0090, Defense Advanced Research Projects Agency grant N00014-91-J-4016, and National Science Foundation grant DMS-92-11820.

PY - 1994/12

Y1 - 1994/12

N2 - A new collocation method for the numerical solution of partial differential equations is presented. This method uses the Chebyshev collocation points, but, because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular L2 estimates can be easily obtained for hyperbolic and parabolic problems.

AB - A new collocation method for the numerical solution of partial differential equations is presented. This method uses the Chebyshev collocation points, but, because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular L2 estimates can be easily obtained for hyperbolic and parabolic problems.

KW - Chebyshev-Legendre

KW - penalty method

KW - differentiation matrix

KW - stability

UR - https://www.scopus.com/pages/publications/0028750042

U2 - 10.1137/0731079

DO - 10.1137/0731079

M3 - Journal article

AN - SCOPUS:0028750042

SN - 0036-1429

VL - 31

SP - 1519

EP - 1534

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 6

ER -

The Chebyshev–Legendre Method: Implementing Legendre Methods on Chebyshev Points

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