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  • 1
    Electronic Resource
    Electronic Resource
    Zur Inversmonotonie diskreter Probleme (1977)
    Springer
    Numerische Mathematik 27 (1977), S. 227-238 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper describes sufficient conditions for a real square matrixA=(a ij ) to have a nonnegative inverse. It is not assumed thata ij ≦0 fori≠j. We indicate several applications to matricesA that occur in finite-difference and finiteelement methods for boundary-value problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396643
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Inverse monotonicity and difference schemes of higher order. A summary for two-point boundary value problems (1979)
    Springer
    Aequationes mathematicae 19 (1979), S. 1-36 
    Details
    ISSN: 1420-8903
    Keywords: Primary 34A50, 65H10, 65L10 ; Secondary 15A48, 34B15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02189843
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  • 3
    Electronic Resource
    Electronic Resource
    Adaptive data distribution for concurrent continuation (1992)
    Springer
    Numerische Mathematik 62 (1992), S. 269-294 
    Details
    ISSN: 0945-3245
    Keywords: 15-04, 15A05 ; 15A12 ; 15A23 ; 34C30 ; 35L50 ; 65-04 ; 65F05 ; 65F35 ; 65Y05 ; 65Y20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Continuation methods compute paths of solutions of nonlinear equations that depend on a parameter. This paper examines some aspects of the multicomputer implementation of such methods. The computations are done on a mesh connected multicomputer with 64 nodes. One of the main issues in the development of concurrent programs is load balancing, achieved here by using appropriate data distributions. In the continuation process, many linear systems have to be solved. For nearby points along the solution path, the corresponding system matrices are closely related to each other. Therefore, pivots which are good for theLU-decomposition of one matrix are likely to be acceptable for a whole segment of the solution path. This suggests to choose certain data distributions that achieve good load balancing. In addition, if these distributions are used, the resulting code is easily vectorized. To test this technique, the invariant manifold of a system of two identical nonlinear oscillators is computed as a function of the coupling between them. This invariant manifold is determined by the solution of a system of nonlinear partial differential equations that depends on the coupling parameter. A symmetry in the problem reduces this system to one single equation, which is discretized by finite differences. The solution of the discrete nonlinear system is followed as the coupling parameter is changed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396229
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Resolvent Estimates and Quantification of Nonlinear Stability (2000)
    Springer
    Acta mathematica sinica 16 (2000), S. 1-20 
    Details
    ISSN: 1000-9574
    Keywords: Key words Resolvent estimates, Nonlinear stability, Pseudospectrum, Convection-dominated flow ; 1991MR Subject Classification 35G20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The aim of this paper is to clarify the role played by resolvent estimates for nonlinear stability. We will give examples showing that a large resolvent may lead to a small domain of nonlinear stability. In other examples the resolvent is large, but the domain of nonlinear stability is completely unrestricted. Which case prevails depends on the details of the problem. We will also show that the size of the resolvent depends in an essential way on the norms that are used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s101140050001
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  • 5
    Electronic Resource
    Electronic Resource
    Lyapunov-type numbers and torus breakdown: numerical aspects and a case study (1997)
    Springer
    Numerical algorithms 14 (1997), S. 79-102 
    Details
    ISSN: 1572-9265
    Keywords: Lyapunov-type numbers ; invariant tori ; coupled oscillator ; phase locking ; 65L
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this work we examine the breakdown mechanism for a 2-torus associated to a system of coupled oscillators. To this end, we rely on computation of the Lyapunov-type numbers, as defined by Fenichel in N. Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J. 21 (1971) 193–226. We give some general results on these numbers, and some specific constructive results for the case in which there is phase-locking on the torus. This is the situation for the system of coupled oscillators we consider, and it leads to great simplifications in the computation of the Lyapunov-type numbers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019100627272
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  • 6
    Electronic Resource
    Electronic Resource
    Book review (1991)
    Springer
    Educational studies in mathematics 22 (1991), S. 87-103 
    Details
    ISSN: 1573-0816
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00302718
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  • 7
    Book
    Book
    Initial-boundary value problems and the Navier-Stokes equations; 136 (1989)
    London u.a. :Academic Press,
    Details
    Title: Initial-boundary value problems and the Navier-Stokes equations; 136
    Author: Kreiss, Heinz-Otto
    Contributer: Lorenz, Jens
    Publisher: London u.a. :Academic Press,
    Year of publication: 1989
    Pages: 402 S.
    Series Statement: Pure and applied mathematics 136
    Type of Medium: Book
    URL: http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0689.35001&format=complete
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    ZIB Catalog
    Zuse Institute Berlin get availability status
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