Article (Scientific journals)
Application of Miller's theorem to the stability analysis of numerical schemes; some useful tools for rapid inspection of discretisations in ocean modelling
Beckers, Jean-Marie
1999In Ocean Modelling, 1, p. 29-37
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Keywords :
Numerical stability
Abstract :
[en] An old theorem about the roots of a polynomial is resurfaced and examined, focusing on the practical question of determining stability criteria for numerical schemes. Is is demonstrated that the theorem can be useful both for analytical studies of the stability limits, as well as numerical searches for stability regions. It is particularly important that when deciding whether the scheme is stable or not, it is not necessary to search for the roots of the polynomial. Indeed, such a decision may be reached through a finite and small number of arithmetic operations and verifications of inequalities. In addition to the analysis of the theorem, some practical conditions for polynomial of different orders are presented, as well as some useful tips on how simply necessary or sufficient stability conditions can be obtained.
Disciplines :
Earth sciences & physical geography
Author, co-author :
Beckers, Jean-Marie  ;  Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > GeoHydrodynamics and Environment Research (GHER)
Language :
English
Title :
Application of Miller's theorem to the stability analysis of numerical schemes; some useful tools for rapid inspection of discretisations in ocean modelling
Publication date :
1999
Journal title :
Ocean Modelling
ISSN :
1463-5003
eISSN :
1463-5011
Publisher :
Elsevier Science, Oxford, United Kingdom
Volume :
1
Pages :
29-37
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 25 February 2010

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