Two-step waveform relaxation methods for implicit linear initial value problems

Jian Yu Pan; Zhong Zhi Bai; Michael K. Ng

doi:10.1002/nla.416

Two-step waveform relaxation methods for implicit linear initial value problems

Jian Yu Pan, Zhong Zhi Bai^*, Michael K. Ng

^*Corresponding author for this work

Department of Mathematics

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

15 Citations (Scopus)

Abstract

A class of two-step waveform relaxation methods is established and studied for solving implicit linear initial value problems, which, in particular, includes the alternating direction implicit waveform relaxation (ADIWR) methods. The convergence property of the ADIWR methods is studied in depth under suitable conditions, and their computing behaviour is illustrated by numerical examples. Moreover, we discuss about the choice of the optimal parameters involved in the ADIWR methods.

Original language	English
Pages (from-to)	293-304
Number of pages	12
Journal	Numerical Linear Algebra with Applications
Volume	12
Issue number	2-3
DOIs	https://doi.org/10.1002/nla.416
Publication status	Published - Mar 2005

Scopus Subject Areas

Algebra and Number Theory
Applied Mathematics

User-Defined Keywords

Alternating direction implicit iteration
Convergence analysis
Initial value problems
Waveform relaxation

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10.1002/nla.416

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@article{21e9667e848144eba061ae59d2f1b95f,

title = "Two-step waveform relaxation methods for implicit linear initial value problems",

abstract = "A class of two-step waveform relaxation methods is established and studied for solving implicit linear initial value problems, which, in particular, includes the alternating direction implicit waveform relaxation (ADIWR) methods. The convergence property of the ADIWR methods is studied in depth under suitable conditions, and their computing behaviour is illustrated by numerical examples. Moreover, we discuss about the choice of the optimal parameters involved in the ADIWR methods.",

keywords = "Alternating direction implicit iteration, Convergence analysis, Initial value problems, Waveform relaxation",

author = "Pan, {Jian Yu} and Bai, {Zhong Zhi} and Ng, {Michael K.}",

note = "Funding Information: The Special Funds for Major State Basic Research Projects. Grant Number: G1999032803 RGC Grants. Grant Numbers: 7046/03P, 7130/02P HKU CRCG Grant. Grant Numbers: 10203501, 10203907, 10203408 Publisher copyright: {\textcopyright} 2004 John Wiley & Sons, Ltd.",

year = "2005",

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doi = "10.1002/nla.416",

language = "English",

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journal = "Numerical Linear Algebra with Applications",

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T1 - Two-step waveform relaxation methods for implicit linear initial value problems

AU - Pan, Jian Yu

AU - Bai, Zhong Zhi

AU - Ng, Michael K.

N1 - Funding Information: The Special Funds for Major State Basic Research Projects. Grant Number: G1999032803 RGC Grants. Grant Numbers: 7046/03P, 7130/02P HKU CRCG Grant. Grant Numbers: 10203501, 10203907, 10203408 Publisher copyright: © 2004 John Wiley & Sons, Ltd.

PY - 2005/3

Y1 - 2005/3

N2 - A class of two-step waveform relaxation methods is established and studied for solving implicit linear initial value problems, which, in particular, includes the alternating direction implicit waveform relaxation (ADIWR) methods. The convergence property of the ADIWR methods is studied in depth under suitable conditions, and their computing behaviour is illustrated by numerical examples. Moreover, we discuss about the choice of the optimal parameters involved in the ADIWR methods.

AB - A class of two-step waveform relaxation methods is established and studied for solving implicit linear initial value problems, which, in particular, includes the alternating direction implicit waveform relaxation (ADIWR) methods. The convergence property of the ADIWR methods is studied in depth under suitable conditions, and their computing behaviour is illustrated by numerical examples. Moreover, we discuss about the choice of the optimal parameters involved in the ADIWR methods.

KW - Alternating direction implicit iteration

KW - Convergence analysis

KW - Initial value problems

KW - Waveform relaxation

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U2 - 10.1002/nla.416

DO - 10.1002/nla.416

M3 - Journal article

AN - SCOPUS:20744441107

SN - 1070-5325

VL - 12

SP - 293

EP - 304

JO - Numerical Linear Algebra with Applications

JF - Numerical Linear Algebra with Applications

IS - 2-3

ER -

Two-step waveform relaxation methods for implicit linear initial value problems

Abstract

Scopus Subject Areas

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