A note on convergence of line iterative methods for a nine-point matrix

S. Karaa; Jun Zhang

doi:10.1016/S0893-9659(01)00164-1

A note on convergence of line iterative methods for a nine-point matrix

S. Karaa^*, Jun Zhang

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We prove the convergence of line iterative methods for solving the linear system arising from a nine-point compact discretization of a special two-dimensional convection diffusion equation. The results provide rigorous justification for the numerical experiments conducted elsewhere, which demonstrate the high accuracy and stability advantages of the fourth-order compact scheme. Numerical experiments are used to support our analytic results.

Original language	English
Pages (from-to)	495-503
Number of pages	9
Journal	Applied Mathematics Letters
Volume	15
Issue number	4
DOIs	https://doi.org/10.1016/S0893-9659(01)00164-1
Publication status	Published - May 2002

Keywords

Convection diffusion equation
Fourth-order compact scheme
Line Jacobi method
Linear systems
Spectral radius

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1016/S0893-9659(01)00164-1

Cite this

@article{e30363d2ada74fe784963d36865a8171,

title = "A note on convergence of line iterative methods for a nine-point matrix",

abstract = "We prove the convergence of line iterative methods for solving the linear system arising from a nine-point compact discretization of a special two-dimensional convection diffusion equation. The results provide rigorous justification for the numerical experiments conducted elsewhere, which demonstrate the high accuracy and stability advantages of the fourth-order compact scheme. Numerical experiments are used to support our analytic results.",

keywords = "Convection diffusion equation, Fourth-order compact scheme, Line Jacobi method, Linear systems, Spectral radius",

author = "S. Karaa and Jun Zhang",

note = "Funding Information: *This autlhor's remmrch was supported by the U.S. National Science Foundation CCR-9988165, and CCR-0043861.",

year = "2002",

month = may,

doi = "10.1016/S0893-9659(01)00164-1",

language = "English",

volume = "15",

pages = "495--503",

journal = "Applied Mathematics Letters",

issn = "0893-9659",

publisher = "Elsevier Limited",

number = "4",

}

TY - JOUR

T1 - A note on convergence of line iterative methods for a nine-point matrix

AU - Karaa, S.

AU - Zhang, Jun

N1 - Funding Information: *This autlhor's remmrch was supported by the U.S. National Science Foundation CCR-9988165, and CCR-0043861.

PY - 2002/5

Y1 - 2002/5

N2 - We prove the convergence of line iterative methods for solving the linear system arising from a nine-point compact discretization of a special two-dimensional convection diffusion equation. The results provide rigorous justification for the numerical experiments conducted elsewhere, which demonstrate the high accuracy and stability advantages of the fourth-order compact scheme. Numerical experiments are used to support our analytic results.

AB - We prove the convergence of line iterative methods for solving the linear system arising from a nine-point compact discretization of a special two-dimensional convection diffusion equation. The results provide rigorous justification for the numerical experiments conducted elsewhere, which demonstrate the high accuracy and stability advantages of the fourth-order compact scheme. Numerical experiments are used to support our analytic results.

KW - Convection diffusion equation

KW - Fourth-order compact scheme

KW - Line Jacobi method

KW - Linear systems

KW - Spectral radius

UR - http://www.scopus.com/inward/record.url?scp=31244436365&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=31244436365&partnerID=8YFLogxK

U2 - 10.1016/S0893-9659(01)00164-1

DO - 10.1016/S0893-9659(01)00164-1

M3 - Article

AN - SCOPUS:31244436365

SN - 0893-9659

VL - 15

SP - 495

EP - 503

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 4

ER -

A note on convergence of line iterative methods for a nine-point matrix

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this