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

Computer Science

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

6 Scopus citations

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
State	Published - May 2002

Bibliographical note

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

Funding

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

Funders	Funder number
National Science Foundation Arctic Social Science Program	CCR-0043861, CCR-9988165
National Science Foundation Arctic Social Science Program

Keywords

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

ASJC Scopus subject areas

Applied Mathematics

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10.1016/S0893-9659(01)00164-1

Cite this

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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.",

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language = "English",

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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 - https://www.scopus.com/pages/publications/31244436365

UR - https://www.scopus.com/pages/publications/31244436365#tab=citedBy

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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

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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