Dynamic Consistency of Discretization
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F12%3A00059584" target="_blank" >RIV/00216224:14310/12:00059584 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Dynamic Consistency of Discretization
Original language description
Numerical methods for solving differential equations transform continuous dynamical systems into discrete ones. We naturally ask whether the dynamics is preserved and for parameter-dependent systems, whether the discretization preserves also bifurcationsof equilibria, limit cycles or basins of attraction. We can study these problems using bifurcation theory and find the critical value of the time-step as a parameter of the discrete system. We find for example that all Runge-Kutta method of the odd order undergo the flip bifurcation of the stable (continuous) equilibria. We usually assume that the dynamics is preserved under discretization of sufficiently small step of the numerical method, but this assumption seems to be excessive.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
V - Vyzkumna aktivita podporovana z jinych verejnych zdroju
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Workshop of the Jaroslav Hájek Center and Financial Mathematics in Practice I, Book of short papers
ISBN
9788021057784
ISSN
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e-ISSN
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Number of pages
6
Pages from-to
69-75
Publisher name
Masaryk University, Brno
Place of publication
Brno
Event location
Jedovnice, Brno
Event date
Sep 14, 2011
Type of event by nationality
CST - Celostátní akce
UT code for WoS article
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