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  • stability
  • Springer  (76)
  • 1985-1989  (76)
  • 1
    Electronic Resource
    Electronic Resource
    Second-order explicit characteristic difference schemes for quasilinear hyperbolic systems (1985)
    Springer
    Computing 35 (1985), S. 85-91 
    Details
    ISSN: 1436-5057
    Keywords: 65M05 ; 65M10 ; 65M25 ; Second order ; characteristic difference schemes ; quasilinear hyperbolic systems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir stellen ein Charakteristikenverfahren zweiter Ordnung für die numerische Lösung der Anfangswertaufgabe von quasilinearen hyperbolischen Systemen vor und beweisen die Stabilität des Verfahrens für Systeme mit konstanten Koeffizienten.
    Notes: Abstract We present two-step, second-order explicit characteristic difference schemes for the numerical solution of initialvalue problems for quasilinear hyperbolic system and show that the method is stable for systems with constant coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02240149
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  • 2
    Electronic Resource
    Electronic Resource
    Nichtlineare Stabilität und Phasenuntersuchung adaptiver Nyström-Runge-Kutta-Methoden (1985)
    Springer
    Computing 35 (1985), S. 325-344 
    Details
    ISSN: 1436-5057
    Keywords: 65L05 ; Numerical analysis ; Nyström methods ; stiff problems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract The stability of adaptive Nyström-Runge-Kutta procedures is studied for a wide class of nonlinear stiff systems of second order differential equations. We show that for a large class of semi-discrete hyperbolic and parabolic problems the restriction of the stepsize is not due to the stiffness of the differential equation. Furthermore we use the scalar test equation $$y'' = - \omega ^2 y + q \cdot e^{iv(t - t_0 )} $$ to derive conditions which ensure that the numerical forced oscillation is in phase with the analytical forced oscillation. The order of adaptive Nyström-Runge-Kutta methods (with a stability-matrix based on a diagonal Padéapproximation) for which the forced oscillation is in phase with its analytical counterpart cannot be greater than two. This barrier of order is not true forr-stage implicit Nyström methods of orderp=2r.
    Notes: Zusammenfassung Für eine umfangreiche Klasse nichtlinearer steifer Differentialgleichungssysteme zweiter Ordnung wird die Stabilität adaptiver Nyström-Runge-Kutta-Verfahren untersucht. Wir zeigen, daß für eine große Klasse semidiskretisierter hyperbolischer und parabolischer Probleme die Restriktion der Schrittweite unabhängig von der Steifheit des Differentialgleichungssystems ist. Weiterhin verwenden wir die skalare Testgleichung $$y'' = - \omega ^2 y + q \cdot e^{iv(t - t_0 )} $$ und geben Bedingungen dafür an, daß die numerische erzwungene Schwingung mit der analytischen erzwungenen Schwingung in Phase ist. Die Konsistenzordnung adaptiver Nyström-Runge-Kutta-Verfahren (mit einer Stabilitätsmatrix, die auf einer diagnolen Padé-Approximation beruht), für die die erzwungene Schwingung mit ihrem analytischen Gegenstück in Phase ist, kann nicht größer als zwei sein. Diese Ordnungsbarriere gilt nicht fürr-stufige implizite Nyström-Methoden der Ordnungp=2r.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02240198
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  • 3
    Electronic Resource
    Electronic Resource
    The interaction of modified 7S soy protein with mono- and di-glycerides at the oil-water interface and its effect on the stability of concentrated corn oil-in-water emulsions (1988)
    Springer
    Colloid & polymer science 266 (1988), S. 930-936 
    Details
    ISSN: 1435-1536
    Keywords: Emulsions ; stability ; interfacial properties of emulsions ; soybean protein ; glycerides ; stabilised O/W emulsions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The influence of chemically modified 7S fraction of soybean protein (7MSPF), and its partial replacement by mono- and di-glycerides in various ratios, on the rate of drop coalescence in concentrated corn oil-in-water emulsions has been investigated. A total emulsifier concentration of 2.0 % (wt/wt) was used. The minimum drop coalescence rate was achieved when using 1.0% (wt/wt) 7MSPF in conjunction with 0.5% (wt/wt) monoglyceride and 0.5 % (wt/wt) di-glyceride at pH 5.5. At other mono-/di-glycerides and protein/glycerides ratios, and at other pHs, the rate of drop coalescence was higher than when 2.0% (wt/wt) 7MSPF was used. The reduction in drop coalescence rate under these conditions is attributed to association of 7MSPF with the glycerides at the oil-water interface. The influence of protein/glycerides ratio on the viscoelastic properties of mixed interfacial films supports this view.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01410849
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  • 4
    Electronic Resource
    Electronic Resource
    Stabilität der ebenen Couette-Strömung eines Maxwell-Fluids und ihre kritische Weissenbergzahl (1987)
    Springer
    Rheologica acta 26 (1987), S. 119-126 
    Details
    ISSN: 1435-1528
    Keywords: Maxwell fluid ; planeCouette flow ; stability ; criticalWeissenberg number
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Abstract The stability behaviour of a Maxwell fluid in a simple plane shear flow for a class of special perturbations is investigated. Necessary and sufficient stability criteria, especially a critical Weissenberg number for the stability (We k ≈ 4) are given. The results of the analysis are in qualitative agreement with experimental observations.
    Notes: Zusammenfassung Es wird das Stabilitätsverhalten eines Maxwell-Fluids in einer einfachen ebenen Scherströmung für eine spezielle Störungsklasse untersucht. Notwendige und hinreichende Stabilitätskriterien sowie eine kritische Weissenbergzahl (We k ≈ 4) werden angegeben. Die Ergebnisse der Analyse stehen mit experimentellen Befunden in qualitativer Übereinstimmung.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01331969
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  • 5
    Electronic Resource
    Electronic Resource
    Methodological problems associated with the Use of the Delphi technique (1987)
    Springer
    Fire technology 23 (1987), S. 175-185 
    Details
    ISSN: 1572-8099
    Keywords: Fire evaluation ; expert ; consensus ; stability ; reliability ; validity ; scaling measurement
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract In this article some of the methodological problems associated with using the Delphi technique for the development of a Firesafety Evaluation (Points) Scheme are examined. These problems relate to: questionnaire design, the merits and demerits of Delphi groups versus panel groups, the definition of key terms (such as expert, consensus and stability), the reliability, validity and level of measurement achieved by Likert-type scaling techniques, and the differences in the decisionmaking processes of expert and nonexpert groups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036934
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  • 6
    Electronic Resource
    Electronic Resource
    The dynamics of coupled planar rigid bodies. II. Bifurcations, periodic solutions, and chaos (1989)
    Springer
    Journal of dynamics and differential equations 1 (1989), S. 269-298 
    Details
    ISSN: 1572-9222
    Keywords: Geometric mechanics ; reduction ; stability ; chaos ; rigid body dynamics ; periodic orbits ; 58F
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053929
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  • 7
    Electronic Resource
    Electronic Resource
    Consumer memory and price fluctuations in commodity markets: An integrodifferential model (1989)
    Springer
    Journal of dynamics and differential equations 1 (1989), S. 299-325 
    Details
    ISSN: 1572-9222
    Keywords: Commodity markets ; time delays ; stability ; Hopf bifurcation ; 34K15 ; 45J05 ; 90A16
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A model for the dynamics of price adjustment in a single commodity market is developed. Nonlinearities in both supply and demand functions are considered explicitly, as are delays due to production lags and storage policies, to yield a nonlinear integrodifferential equation. Conditions for the local stability of the equilibrium price are derived in terms of the elasticities of supply and demand, the supply and demand relaxation times, and the equilibrium production-storage delay. The destabilizing effect of consumer memory on the equilibrium price is analyzed, and the ensuing Hopf bifurcations are described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053930
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  • 8
    Electronic Resource
    Electronic Resource
    Derivative free multipoint iterative methods for simple and multiple roots (1986)
    Springer
    BIT 26 (1986), S. 93-99 
    Details
    ISSN: 1572-9125
    Keywords: Primary 65HO5 ; nonlinear equation ; multiple roots ; multipoint iterative methods ; error constant ; stability ; efficiency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A one-parameter family of derivative free multipoint iterative methods of orders three and four are derived for finding the simple and multiple roots off(x)=0. For simple roots, the third order methods require three function evaluations while the fourth order methods require four function evaluations. For multiple roots, the third order methods require six function evaluations while the fourth order methods require eight function evaluations. Numerical results show the robustness of these methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01939365
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  • 9
    Electronic Resource
    Electronic Resource
    A note on contractivity in the numerical solution of initial value problems (1987)
    Springer
    BIT 27 (1987), S. 424-437 
    Details
    ISSN: 1572-9125
    Keywords: 65 L 05 ; 65 L 20 ; stability ; contractivity ; numerical solution of stiff initial value problems in ordinary differential equations ; Runge-Kutta methods ; Rosenbrock methods ; rational Runge-Kutta methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper concerns the stability analysis of numerical methods for approximating the solutions to (stiff) initial value problems. Our analysis includes the case of (nonlinear) systems of differential equations that are essentially more general than the classical test equationU′=λU, with λ a complex constant. We explore the relation between two stability concepts, viz. the concepts of contractivity and weak contractivity. General Runge-Kutta methods, one-stage Rosenbrock methods and a notable rational Runge-Kutta method are analysed in some detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01933735
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  • 10
    Electronic Resource
    Electronic Resource
    Growth and long-run stability (1987)
    Springer
    Acta applicandae mathematicae 9 (1987), S. 219-237 
    Details
    ISSN: 1572-9036
    Keywords: 34A34 ; 34D99 ; 90A16 ; Nonlinear differential equations ; stability ; growth ; economic dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00047540
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