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  • 1
    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
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  • 2
    Digitale Medien
    Digitale Medien
    A Direct Approach to Homoclinic Orbits in the Fast Dynamics of Singularly Perturbed Systems (1999)
    Springer
    Journal of dynamics and differential equations 11 (1999), S. 671-709 
    Details
    ISSN: 1572-9222
    Schlagwort(e): Homoclinic orbits ; singular perturbations ; bifurcation ; FitzHugh–Nagumo system
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Homoclinic orbits in the fast dynamics of singular perturbation problems are usually analyzed by a combination of Fenichel's invariant manifold theory with general transversality arguments (see Ref. 29 and the Exchange Lemma in Ref. 16). In this paper an alternative direct approach is developed which uses a two-time scaling and a contraction argument in exponentially weighted spaces. Homoclinic orbits with one last transition are treated and it is shown how ε-expansions can be extracted rigorously from this approach. The result is applied to a singularity perturbed Bogdanov point in the FitzHugh–Nagumo system.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022663512855
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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