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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

  • DOI - Digital Object Identifier

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

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

  • 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

  • e-ISSN

  • 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