Unconditionally stable ADI scheme of higher-order for linear hyperbolic equations

Samir Karaa

doi:10.1080/00207160902878548

Unconditionally stable ADI scheme of higher-order for linear hyperbolic equations

Samir Karaa^*

^*Corresponding author for this work

Mathematics

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

27 Citations (Scopus)

Abstract

An unconditionally stable alternating direction implicit (ADI) method of higher-order in space is proposed for solving two- and three-dimensional linear hyperbolic equations. The method is fourth-order in space and second-order in time. The solution procedure consists of a multiple use of one-dimensional matrix solver which produces a computational cost effective solver. Numerical experiments are conducted to compare the new scheme with the existing scheme based on second-order spatial discretization. The effectiveness of the new scheme is exhibited from the numerical results.

Original language	English
Pages (from-to)	3030-3038
Number of pages	9
Journal	International Journal of Computer Mathematics
Volume	87
Issue number	13
DOIs	https://doi.org/10.1080/00207160902878548
Publication status	Published - Oct 2010

Keywords

ADI method
high-order difference scheme
hyperbolic equation
unconditional stability

ASJC Scopus subject areas

Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

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10.1080/00207160902878548

Cite this

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title = "Unconditionally stable ADI scheme of higher-order for linear hyperbolic equations",

abstract = "An unconditionally stable alternating direction implicit (ADI) method of higher-order in space is proposed for solving two- and three-dimensional linear hyperbolic equations. The method is fourth-order in space and second-order in time. The solution procedure consists of a multiple use of one-dimensional matrix solver which produces a computational cost effective solver. Numerical experiments are conducted to compare the new scheme with the existing scheme based on second-order spatial discretization. The effectiveness of the new scheme is exhibited from the numerical results.",

keywords = "ADI method, high-order difference scheme, hyperbolic equation, unconditional stability",

author = "Samir Karaa",

note = "Funding Information: This research was supported by Sultan Qaboos University under Grant IG/SCI/DOMAS/07/08.",

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N1 - Funding Information: This research was supported by Sultan Qaboos University under Grant IG/SCI/DOMAS/07/08.

PY - 2010/10

Y1 - 2010/10

N2 - An unconditionally stable alternating direction implicit (ADI) method of higher-order in space is proposed for solving two- and three-dimensional linear hyperbolic equations. The method is fourth-order in space and second-order in time. The solution procedure consists of a multiple use of one-dimensional matrix solver which produces a computational cost effective solver. Numerical experiments are conducted to compare the new scheme with the existing scheme based on second-order spatial discretization. The effectiveness of the new scheme is exhibited from the numerical results.

AB - An unconditionally stable alternating direction implicit (ADI) method of higher-order in space is proposed for solving two- and three-dimensional linear hyperbolic equations. The method is fourth-order in space and second-order in time. The solution procedure consists of a multiple use of one-dimensional matrix solver which produces a computational cost effective solver. Numerical experiments are conducted to compare the new scheme with the existing scheme based on second-order spatial discretization. The effectiveness of the new scheme is exhibited from the numerical results.

KW - ADI method

KW - high-order difference scheme

KW - hyperbolic equation

KW - unconditional stability

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Unconditionally stable ADI scheme of higher-order for linear hyperbolic equations

Abstract

Keywords

ASJC Scopus subject areas

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