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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
    Sequence analysis of the cystic fibrosis gene in patients with disseminated bronchiectatic lung disease (1991)
    Springer
    Journal of molecular medicine 69 (1991), S. 657-663 
    Details
    ISSN: 1432-1440
    Keywords: Polymerase chain reaction ; Direct genomic DNA sequencing ; Automated DNA sequencing ; Cystic fibrosis gene ; Bronchiectatic lung disease
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary The diagnosis of classical cystic fibrosis (CF) is easily made by clinical assessment alone, but may be missed or delayed in cases with an atypical clinical course. In a recent major study the age at diagnosis varied between 2 months and 47 years. For diagnostic purposes we have investigated the cystic fibrosis transmembrane regulator (CFTR) gene in 10 adult patients (age 18 to 45 years) with chronic obstructive pulmonary disease since childhood or adolescence and bronchiectases disseminated through both lungs. Only one subject (a 29-year-old male) had exocrine pancreatic insufficiency (PI); all others were pancreatic-sufficient (PS). The first nucleotide (ATP)-binding fold of the CFTR was analyzed by direct sequencing of polymerase chain reaction (PCR)-amplified genomic DNA in these cases. Two patients with different phenotypes (one PI, one PS) were found to be homozygous for the common ΔF508 mutation of the CFTR gene, which proved the diagnosis of cystic fibrosis in their cases and allowed genetic counselling. The PS patient had normal sweat tests and had not previously been recognized as having CF. Four other patients were heterozygous for ΔF508, with no other mutation in exons 10 or 11 of the gene, and four patients had normal sequences of these exons. Because only about 70% of all CF chromosomes carry ΔF508, the unexpectedly high frequency (4/8=50%) of heterozygosity for ΔF508 among the non-ΔF508/ΔF508 patients with bronchiectases suggests that some of these might also have unrecognized CF with rare genotypes and mutations in any of the 22 exons not sequenced. About 90 different mutations have already been detected in coding regions of the CFTR gene and a very broad and so far not fully recognized spectrum of clinical phenotypes may be caused by mutations of this gene. Screening for the most frequent CFTR gene mutations, which is practicable using recent technology, may provide significant new diagnostic information in patients with CF-like pulmonary phenotypes, especially if they have normal or borderline sweat tests and no pancreatic insufficiency.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01649427
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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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