Bibliothek

X
feed icon rss

Ihre E-Mail wurde erfolgreich gesendet. Bitte prüfen Sie Ihren Maileingang.

Leider ist ein Fehler beim E-Mail-Versand aufgetreten. Bitte versuchen Sie es erneut.

Vorgang fortführen?

Exportieren
  • 1
    Digitale Medien
    Digitale Medien
    On invariant closed curves for one-step methods (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 103-122 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS) 65L05, 58F08, 58F22 ; CR: G1.7
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We show that a one-step method as applied to a dynamical system with a hyperbolic periodic orbit, exhibits an invariant closed curve for sufficiently small step size. This invariant curve converges to the periodic orbit with the order of the method and it inherits the stability of the periodic orbit. The dynamics of the one-step method on the invariant curve can be described by the rotation number for which we derive an asymptotic expression. Our results complement those of [2, 3] where one-step methods were shown to create invariant curves if the dynamical system has a periodic orbit which is stable in either time direction or if the system undergoes a Hopf bifurcation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01399697
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    Artikel (Nationallizenzen)
    Volltext
  • 2
    Digitale Medien
    Digitale Medien
    Zur Stabilität von Differenzenverfahren für Systeme linearer gewöhnlicher Randwertaufgaben (1978)
    Springer
    Numerische Mathematik 29 (1978), S. 209-226 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65L 10 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In this paper we give a simple stability theory for finite difference approximations to linear ordinary boundary value problems. In particular we consider stability with respect to a maximum norm including all difference quotients up to the order of the differential equation. It is shown that stability in this sense holds if and only if the principal part of the differential equation is discretized in a “stable way”. This last property is characterized by root conditions which we prove to be satisfied for some classes of finite difference schemes. Our approach simplifies and generalizes some known results of the literature where Sobolev norms or merely the maximum norm are used.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01390339
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    Artikel (Nationallizenzen)
    Volltext
Schließen ⊗
Diese Webseite nutzt Cookies und das Analyse-Tool Matomo. Weitere Informationen finden Sie hier...