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  • 1
    Electronic Resource
    Electronic Resource
    A constructive method of solving the Liapounov equation for complex matrices (1972)
    Springer
    Numerische Mathematik 19 (1972), S. 433-438 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper describes a method of solving the Liapounov equation (1)HM+M * H=2D, M in upper Hessenberg form,D diagonal. Initialising the first row of the matrixA arbitrarily, one can find (by solving equations with one unknown) the unknown elements ofA such that (2)AM+M * A * =2F, whereA differs from a Hermitian matrix only in that its diagonal elements need not be real.F is a diagonal matrix which is uniquely determined by the first row ofA. By solving Eq. (2) for several initial values one may generate several matricesA andF (in the most unfavourable case 2n−1A's andF's are needed) and superpose them to getn linearly independent Hermitian matricesH j andD j respectively for whichH j M+M * H j =2D j is valid. Then one can solve the real system $$\sum\limits_{j = 1}^n {p_j D_j } = D$$ to obtain the solution $$H: = \sum\limits_{j = 1}^n {p_j ,} H_j$$ of Eq. (1).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01404926
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  • 2
    Electronic Resource
    Electronic Resource
    A note on the approximation of mildly nonlinear Dirichlet problems by finite differences (1979)
    Springer
    Numerische Mathematik 33 (1979), S. 303-313 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N20 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In [9], Simpson proved some theorems concerning the approximation of mildly nonlinear Dirichlet problems −Δu=f (x, u) inD, u=0 on ∂D by finite differences. The assumptionsf(x, 0)≧0 andf u(x, u)〉0 in [9] have turned out to be unnecessarily restrictive and are eliminated in this paper. On the other hand, we considered it necessary to make the smoothness conditions forD slightly more stringent irrespective of the conditions imposed onf.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398646
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  • 3
    Electronic Resource
    Electronic Resource
    Discretization errors at free boundaries of the Grad-Schlüter-Shafranov equation (1991)
    Springer
    Numerische Mathematik 59 (1991), S. 683-710 
    Details
    ISSN: 0945-3245
    Keywords: 65N12 ; 65N06 ; 35J60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The numerical error of standard finite-difference schemes is analyzed at free boundaries of the Grad-Schlüter-Shafranov equation of plasma physics. A simple correction strategy is devised to eliminate (to leading order) the errors which arise as the free boundary crosses the rectangular grid at irregular locations. The resulting scheme can be solved by Gauss-Newton or Inverse iterations, or by multigrid iterations. Extrapolation (from 2nd to 3rd order of accuracy) is possible for the new scheme.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385804
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  • 4
    Electronic Resource
    Electronic Resource
    Some bifurcation diagrams for Taylor vortex flows (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 1248-1252 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The numerical continuation and bifurcation methods of Keller [H. B. Keller, in Applications of Bifurcation Theory (Academic, New York, 1977), pp. 359–384] are used to study the variation of some branches of axisymmetric Taylor vortex flow as the wavelength in the axial direction changes. Closed "loops'' of solutions and secondary bifurcations are determined. Variations with respect to Reynolds number show the same phenomena. The results presented here show that Taylor vortices with periodic boundary conditions exist in a wider range of wavelengths, λ, than observed in the Burkhalter/Koschmieder experiments [Phys. Fluids 17, 1929 (1974)]. They also show that there is possibly a λ subinterval within the neutral curve of Couette flow such that there are no Taylor vortex flows with smallest period in this interval.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865007
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  • 5
    Electronic Resource
    Electronic Resource
    Computation of transitions in Taylor vortex flows (1981)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 32 (1981), S. 710-720 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Die sehr zuverlässigen numerischen Methoden von [15, 18] wurden zur Berechnung von axialsymmetrischen Strömungen zwischen unbeschränkt langen, rotierenden Zylindern benutzt. So wurden Lösungen gefunden, die aus Wirbeln unterschiedlicher Größen bestehen. Durch Variation der Wellenlänge der Wirbel und der Reynoldszahl wurde gezeigt, daß diese Lösungen Übergangszustände sind zwischen verschiedenen Lösungen mit Wirbeln einheitlicher Größe (Übergänge von 2 zu 4 und von 2 zu 6 Wirbeln).
    Notes: Abstract The very reliable numerical methods of [15, 18] were used for the investigation of axisymmetric flows between infinitely long rotating cylinders. Solutions consisting of vortices of different sizes were detected. Varying both the wavelength of the vortices and the Reynolds number, we showed that the solutions are intermediate states between solutions with equally sized vortices (transitions from 2 to 4 and from 2 to 6 vortices).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00946981
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  • 6
    Electronic Resource
    Electronic Resource
    On the decay of symmetric dynamo fieldsThis work was performed under the terms of the agreement on association between the Max-Planck-Institut for Plasmaphysik and EURATOM. (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 91-97 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The ‘anti-dynamo’ theorems for poloidal magnetic fields with axisymmetry and plane symmetry are generalized to the case of a compressible and time-dependent flow in a fluid with arbitrary conductivity.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040107
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  • 7
    Book
    Book
    Pattern formation in viscous-flows : the Taylor-Couette problem and Rayleigh-Benard convection; 128 (1999)
    Basel u.a. :Birkhäuser,
    Details
    Title: Pattern formation in viscous-flows : the Taylor-Couette problem and Rayleigh-Benard convection; 128
    Author: Meyer-Spasche, Rita
    Publisher: Basel u.a. :Birkhäuser,
    Year of publication: 1999
    Pages: 209 S.
    Series Statement: International series of numerical mathematics 128
    Type of Medium: Book
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    Zuse Institute Berlin get availability status
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