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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Computing 50 (1993), S. 213-227 
    ISSN: 1436-5057
    Keywords: 65R20 ; 65L06 ; 45L10 ; Volterra integral equations with delay ; collocation ; continuous Runge-Kutta methods ; superconvergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Diese Arbeit befaßt sich mit Fragen der (lokalen) Superkonvergenz bei Kollokationsverfahren und stetigen impliziten Runge-Kutta-Methoden für Volterrasche Integralgleichungen mit retardiertem Argument. Es wird insbesondere gezeigt, daß (im Gegensatz zu retardierten Differentialgleichungen) Kollokation an den Gauss-Punkten nicht zu einer höheren Konvergenzordnung führt and daß deshalbm-stufige Gauss-Runge-Kutta-Methoden nicht die Ordnungp=2m besitzen.
    Notes: Abstract In the following we give an analysis of the local superconvergence properties of piecewise polynomial collocation methods and related continuous Runge-Kutta-type methods for Volterra integral equations with constant delay. We show in particular that (in contrast to delay differential equations) collocation at the Gauss points does not lead to higher-order convergence and thusm-stage Gauss-Runge-Kutta methods for delay Volterra equations do not possess the orderp=2m.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Computing 40 (1988), S. 125-137 
    ISSN: 1436-5057
    Keywords: 65R20 ; 45J05 ; Volterra integro-differential equations ; collocation approximations ; polynomial spline functions ; optimal discrete convergence order
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Diese Arbeit behandelt die numerische Lösung von Volterraschen Integrodifferential-gleichungenr-ter Ordnung, deren Kernfunktion dier-te Ableitung der gesuchten Lösung enthält, mittels Spline-Funktionen. In Mittelpunkt der Arbeit steht die Frage der optimalen diskreten Konvergenzordnung an den Knoten der approximierenden Spline-Funktion.
    Notes: Abstract We study the application of certain spline collocation methods to Volterra integro-differential equations of orderr where ther-th order derivative of the unknown solution occurs also in the kernel of the integral term. The analysis focuses on the question of the optimal discrete convergence order (at the knots of the approximating spline function).
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Plant and soil 82 (1984), S. 407-413 
    ISSN: 1573-5036
    Keywords: Carbon partitioning ; Field bean ; Mutant lines ; Nitrogen partitioning ; 15N-tracer techniques ; Symbiotic nitrogen fixation ; Vicia faba minor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Homozygous mutant lines of field bean selected for (a) improved yielding potential and (b) altered plant architecture and/or physiological response were tested for symbiotic nitrogen fixing ability under field conditions in comparison with their parent cultivar.15N-tracer techniques were applied to determine %N derived from atmosphere. Data were collected on assimilate and nitrogen accumulation and distribution among various plant parts during two stages of reproductive growth. Symbiotic nitrogen fixation was closely correlated with total plant top biomass and nitrogen yield. A similar close association was found between crop yield and nitrogen harvest index. Both harvest indices tended to be negatively correlated with stage of maturity and with the amount of N derived from air per unit of area. The generally high %N derived from symbiotic N2 fixation and its comparatively small variability implies that this parameter may be difficult to improve inVicia faba under field conditions. It is concluded, that the main genetic potential for improving the amount of biological nitrogen fixation in this crop depends upon factors that promote high photosynthetic productivity and efficient N-use under appropriate agronomic conditions and with effective rhizobial associations. The establishment of rational ideotypes with a possitive impact on yield appears to be of practical significance for increasing the amount of symbiotically fixed nitrogen.
    Type of Medium: Electronic Resource
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