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Two‐step waveform relaxation methods for implicit linear initial value problems
Author(s) -
Pan JianYu,
Bai ZhongZhi,
Ng Michael K.
Publication year - 2004
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.416
Subject(s) - waveform , relaxation (psychology) , convergence (economics) , mathematics , initial value problem , value (mathematics) , class (philosophy) , property (philosophy) , numerical analysis , mathematical optimization , algorithm , mathematical analysis , computer science , statistics , psychology , social psychology , telecommunications , radar , artificial intelligence , economics , economic growth , philosophy , epistemology
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. Copyright © 2004 John Wiley & Sons, Ltd.