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  • 1
    Electronic Resource
    Electronic Resource
    Order barriers for the B-convergence of ROW methods (1989)
    Springer
    Computing 41 (1989), S. 219-235 
    Details
    ISSN: 1436-5057
    Keywords: 65L05 ; Numerical analysis ; stiff problems ; Rosenbrock methods ; B-convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden die Konvergenzeigenschaften der ROW-Verfahren bei ihrer Anwendung auf das steife Differentialgleichungsmodell von Prothero und Robinson untersucht. Dabei zeigt es sich, daß es Barrieren für die tatsächlich erreichbare Konvergenzordnung gibt. Ferner existieren ROW-Verfahren, deren Genauigkeit asymptotisch mit der Steifheit des Modells zunimmt. Die theoretischen Ergebnisse werden an numerischen Beispielen demonstriert.
    Notes: Abstract The convergence of ROW methods is studied when these methods are applied to the stiff model equation of Prothero and Robinson. It turns out that there are barriers of the attainable order of convergence. Furthermore, the existence of ROW methods is shown the accuracy of which increases asymptotically with the stiffness of the model. The theoretical results are demonstrated by numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02259094
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Acute and chronic neuroborreliosis with and without CNS involvement: a clinical, MRI, and HLA study of 27 cases (1991)
    Springer
    Journal of neurology 238 (1991), S. 271-280 
    Details
    ISSN: 1432-1459
    Keywords: Acute neuroborreliosis ; Chronic neuroborreliosis ; Central nervous system ; Magnetic resonance imaging ; HLA studies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary Of the 96 serologically confirmed neuroborreliosis cases seen in our clinic between 1983 and 1988, 11 patients had mild to moderate and 4 patients had serious cerebral and/or spinal cord symptoms. Nine of these 15 patients with CNS involvement exhibited a primary chronic course of the illness. After high-dose intravenous therapy with penicillin, doxycycline or cefotaxime, given mostly in combination with cortisone, gradual recovery occurred with normalization of CSF findings characteristic of neuroborreliosis, and normalization of significantly elevated Borrelia burgdorferi IgG antibody titres in CSF and serum. Brain MRI and CT showed evidence of or were suggestive of vascular involvement which correlated with clinical symptoms in 11 of the 15 patients with CNS involvement. Brain MRI changes that were similar but much slighter in number and intensity were seen in 5 of 12 neuroborreliosis patients without clinical signs of CNS involvement (lymphocytic meningoradiculitis; Bannwarth's syndrome). The frequencies of the HLA-DR7 (75%), HLA-B44 (50%) and HLA-A29 (33%) antigens in 12 neuroborreliosis patients with clinical symptoms of CNS involvement were significantly different from the frequencies in 12 neuroborreliosis patients without CNS involvement and in 100 control subjects. Diagnostic criteria of active neuroborreliosis are proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00319739
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Directional approximation of the jacobians in ROW-methods (1991)
    Springer
    BIT 31 (1991), S. 89-101 
    Details
    ISSN: 1572-9125
    Keywords: 65L05 ; Numerical analysis ; stiff problems ; Rosenbrock methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper a new technique for avoiding exact Jacobians in ROW methods is proposed. The Jacobiansf' n are substituted by matricesA n satisfying a directional consistency conditionA n f n =f' n f n +O(h). In contrast to generalW-methods this enables us to reduce the number of order conditions and we construct a 2-stage method of order 3 and families of imbedded 4-stage methods of order 4(3). The directional approximation of the Jacobians has been realized via rank-1 updating as known from quasi-Newton methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01952786
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On Stetter's global error estimation in the smooth phase of stiff differential equations (1986)
    Springer
    Computing 36 (1986), S. 43-55 
    Details
    ISSN: 1436-5057
    Keywords: 65L05 ; Numerical analysis ; stiff problems ; global error estimation ; Rosenbrock methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Durch Anwendung der 2stufigen ROW-Verfahren auf ein steifes Modellproblem wird die Wirkungsweise der globalen Fehlerschätzung von Stetter in der glatten Phase untersucht. Es zeigt sich, daß diese Fehlerschätzung, die auf derh→0-Asymptotik basiert, bei einer gewissen Wahl der Verfahrensparameter auch fürh≫0 zuverlässig bleibt. Die Zusammenhänge zwischen der Güte der Fehlerschätzung, der Steifheit des Problems und den Parametern des Verfahrens werden mit Hilfe einer Fehlerentwicklung untersucht, deren Koeffizienten sowohl fürh→0 als auch für beliebig wachsende Steifheit beschränkt bleiben. Die theoretischen Ergebnisse werden an zwei numerischen Beispielen demonstriert.
    Notes: Abstract By means of the 2-stage ROW methods, applied to a stiff model, Stetter's global error estimation is studied in the smooth phase. It turns out that this error estimation, which is based on theh→0 asymptotic, remains also reliable forh≫0 if the parameters of the method are chosen in a certain way. The relations between the effectiveness of the error estimation, the stiffness of the problem and the parameters of the method are investigated by means of an error expansion, the coefficients of which are bounded for decreasingh as well as for increasing stiffness. The theoretical results are demonstrated by two numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238191
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    Paper (German National Licenses)
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