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  • 1
    Electronic Resource
    Electronic Resource
    An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation (1997)
    Springer
    Numerische Mathematik 75 (1997), S. 319-337 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65N50, 49L25, 49M25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. In this paper an adaptive finite difference scheme for the solution of the discrete first order Hamilton-Jacobi-Bellman equation is presented. Local a posteriori error estimates are established and certain properties of these estimates are proved. Based on these estimates an adapting iteration for the discretization of the state space is developed. An implementation of the scheme for two-dimensional grids is given and numerical examples are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050241
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A Uniform Exponential Spectrum for Linear Flows on Vector Bundles (2000)
    Springer
    Journal of dynamics and differential equations 12 (2000), S. 435-448 
    Details
    ISSN: 1572-9222
    Keywords: linear flows ; spectral theory ; Morse spectrum ; Lyapunov spectrum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For linear flows on vector bundles we define a uniform exponential spectrum. For a compact invariant set for the projected flow we obtain this spectrum by taking all accumulation points for the time tending to infinity of the union over the finite time exponential growth rates for all initial values in this set. Using direct arguments we show that for a connected compact invariant set this spectrum is a closed interval whose boundary points are Lyapunov exponents. For a compact invariant set on which the flow is chain transitive we show that this spectrum coincides with the Morse spectrum. In particular, this approach admits a straightforward analytic proof for the regularity and continuity properties of the Morse spectrum without using cohomology or ergodicity results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009024610394
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    Paper (German National Licenses)
    Fulltext
  • 3
    Book
    Book
    Gewöhnliche Differentialgleichungen / (2009)
    Wiesbaden :Vieweg + Teubner,
    Details
    Title: Gewöhnliche Differentialgleichungen /
    Author: Grüne, Lars
    Contributer: Junge, Oliver
    Edition: 1. Aufl
    Publisher: Wiesbaden :Vieweg + Teubner,
    Year of publication: 2009
    Pages: XI, 243 S. : , graph. Darst. ; , 210 mm x 148 mm
    Series Statement: Bachelorkurs Mathematik
    ISBN: 978-3-8348-0381-8
    Type of Medium: Book
    Language: German
    Parallel Title: Gewöhnliche Differentialgleichungen
    URL: http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1175.34001
    URL: lizenzfrei
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