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

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

15 Scopus citations

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
State	Published - Mar 2005
Externally published	Yes

Keywords

Alternating direction implicit iteration
Convergence analysis
Initial value problems
Waveform relaxation

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10.1002/nla.416

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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.\}",

year = "2005",

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AU - Bai, Zhong Zhi

AU - Ng, Michael K.

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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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JO - Numerical Linear Algebra with Applications

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ER -

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

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Keywords

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