| PŘIBYLOVÁ, Lenka. Dynamic Consistency of Discretization. In Masaryk University, Brno. Workshop of the Jaroslav Hájek Center and Financial Mathematics in Practice I, Book of short papers. Brno: Masaryk University, Brno, 2012, s. 69-75, 6 s. ISBN 978-80-210-5778-4. |
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@inproceedings{977261,
author = {Přibylová, Lenka},
address = {Brno},
booktitle = {Workshop of the Jaroslav Hájek Center and Financial Mathematics in Practice I, Book of short papers},
editor = {Masaryk University, Brno},
keywords = {discretization; bifurcation},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Brno},
isbn = {978-80-210-5778-4},
pages = {69-75},
publisher = {Masaryk University, Brno},
title = {Dynamic Consistency of Discretization},
year = {2012}
}
TY - JOUR
ID - 977261
AU - Přibylová, Lenka
PY - 2012
TI - Dynamic Consistency of Discretization
PB - Masaryk University, Brno
CY - Brno
SN - 9788021057784
KW - discretization
KW - bifurcation
N2 - 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 bifurcations of 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.
ER -
PŘIBYLOVÁ, Lenka. Dynamic Consistency of Discretization. In Masaryk University, Brno. \textit{Workshop of the Jaroslav Hájek Center and Financial Mathematics in Practice I, Book of short papers}. Brno: Masaryk University, Brno, 2012, s.~69-75, 6 s. ISBN~978-80-210-5778-4.
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