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  • CR: 5.17  (43)
  • 04. Solid Earth::04.03. Geodesy::04.03.01. Crustal deformations
  • GPS
  • Springer  (43)
  • American Society of Hematology
  • Blackwell Publishing
  • Blackwell Publishing Ltd
  • Nature Publishing Group
  • 2005-2009
  • 1980-1984  (43)
  • 1965-1969
  • 1984  (19)
  • 1980  (24)
Collection
Keywords
Publisher
  • Springer  (43)
  • American Society of Hematology
  • Blackwell Publishing
  • Blackwell Publishing Ltd
  • Nature Publishing Group
Years
  • 2005-2009
  • 1980-1984  (43)
  • 1965-1969
Year
  • 1
    Electronic Resource
    Electronic Resource
    Numerische Lösung gewöhnlicher Differentialgleichungen mit Splinefunktionen (1980)
    Springer
    Computing 25 (1980), S. 317-335 
    Details
    ISSN: 1436-5057
    Keywords: AMS (MOS): 65L65 ; CR: 5.17 ; AMS (MOS): 65L65 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract In this paper a general procedure to obtain spline approximations for the solutions of initial value problems for ordinary differential equations is presented. Several well-known spline approximation methods are included as special cases. It is common practice to partition the interval for which the initial value problem is defined into equidistant subintervals and to construct successively the spline approximation; thereby the spline function has to satisfy certain conditions at the knots. In the general procedure presented here additional knots are admitted in every subinterval. At these points which need not be equally spaced the spline approximation has to fulfill analogous conditions as at the original knots. Convergence and divergence theorems are proved; especially the influence of the additional knots on convergence and divergence of the method is investigated.
    Notes: Zusammenfassung In dieser Arbeit wird ein allgemeines Verfahren zur Erzeugung von Splineapproximationen für die Lösungen von Anfangswertproblemen bei gewöhnlichen Differentialgleichungen vorgestellt. Einige der bekannten Spline-approximationsmethoden sind als Spezialfälle enthalten. Eine gängige Vorgehensweise besteht darin, das Intervall, über dem das Anfangswertproblem gegeben ist, in äquidistante Teilintervalle zu zerlegen und dann sukzessive die Splineapproximation zu definieren. Hierbei wird gefordert, daß die Spline-approximation in den Knoten gewisse Bedingungen erfüllt. Bei dem hier betrachteten allgemeinen Verfahren werden in den einzelnen Teilintervallen noch zusätzliche Zwischenknoten eingeführt. In diesen Punkten, die nicht äquidistant sein müssen, werden für die Splineapproximation analoge Bedingungen wie in den Hauptknoten vorgeschrieben. Konvergenz- und Divergenzsätze werden bewiesen, insbesondere wird der Einfluß der Zwischenknoten auf Konvergenz und Divergenz des Verfahrens untersucht.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02285227
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  • 2
    Electronic Resource
    Electronic Resource
    A potential method for the biharmonic equation (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 105-119 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new formulation of the Dirichlet problem for the biharmonic operator is presented. This gives rise to a simple numerical method to solve the above problem. Convergence is proved in the unidimensional case. Numerical results in one and two dimensional test problems are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389641
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  • 3
    Electronic Resource
    Electronic Resource
    A uniformly convergent difference scheme for a semilinear singular perturbation problem (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 175-198 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 L 10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present a difference scheme for solving a semilinear singular perturbation problem with any number of turning points of arbitrary orders. It is shown that a solution of the scheme converges, uniformly in a perturbation parameter, to that of the continuous problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390122
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  • 4
    Electronic Resource
    Electronic Resource
    Une méthode numérique pour les problèmes d'équilibre de corps hyperélastiques compressibles en grandes déformations (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 199-224 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary This paper uses Augmented Lagrangian techniques for the numerical solution of equilibrium problems of compressible hyperelastic bodies subjected to large deformations. The resulting method is illustrated by several numerical examples.
    Notes: Résumé Cet article applique les techniques de Lagrangien Augmenté à la résolution numérique des problèmes d'équilibre de corps hyperélastiques compressibles soumis à de grandes déformations. La méthode obtenue est illustrée par plusieurs exemples numériques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390123
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  • 5
    Electronic Resource
    Electronic Resource
    On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 235-246 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A class of extended backward differentiation formulae suitable for the approximate numerical integration of stiff systems of first order ordinary differential equations is derived. An algorithm is described whereby the required solution is predicted using a conventional backward differentiation scheme and then corrected using an extended backward differentiation scheme of higher order. This approach allows us to developL-stable schemes of order up to 4 andL(α)-stable schemes of order up to 9. An algorithm based on the integration formulae derived in this paper is illustrated by some numerical examples and it is shown that it is often superior to certain existing algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396701
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  • 6
    Electronic Resource
    Electronic Resource
    An approximation theorem for second-order evolution equations (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 127-142 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 34G05, 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A class of approximation schemes of arbitrary accuracy, generated by a two-step recurrence relation, is devised for evolution equations of the second order. The schemes are effected via a specially constructed family of rational approximations to cos τ for τ≧0 and yield computationally efficient methods for systems of second-order ordinary differential equations and semidiscrete approximations for initial-boundary value problems for second-order hyperbolic equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396311
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  • 7
    Electronic Resource
    Electronic Resource
    Méthodes multipas pour des équations paraboliques non linéaires (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 143-162 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65M15, 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study the error due to the discretization in time of a nonlinear parabolic problem by a multistep method. Error estimates are obtained if the method is of the orderp (p〉1) and stronglyA(Θ)-stable $$\left( {0〈 \Theta〈 \frac{\pi }{2}} \right)$$ . The method is also applied to the Navier-Stokes equations in two dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396312
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  • 8
    Electronic Resource
    Electronic Resource
    Enlarging the domain of convergence for multiple shooting by the homotopy method (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 231-240 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The homotopy method is a frequently used technique in overcoming the local convergence nature of multiple shooting. In this paper sufficient conditions are given that guarantee the homotopy process to be feasible. The results are applicable to a class of two-point boundary value problems. Finally, the numerical solution of two practical problems arising in physiology is described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396319
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  • 9
    Electronic Resource
    Electronic Resource
    Une méthode multipas implicite-explicite pour l'approximation des équations d'évolution paraboliques (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 257-276 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65M10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Résumé Considérons une équation d'évolution parabolique linéaire associée à un opérateur linéaireA(t) dépendant du tempst. Nous développons dans cet article une méthode de discrétisation, basée sur les méthodes linéaires à pas multiples, traitant de manière implicite une partie de l'opérateurA(t) indépendante du temps, l'autre partie est traitée de manière explicite. Nous étudions la stabilité et la convergence de cette méthode.
    Notes: Summary Let us consider a linear parabolic equation which is associated with a time dependent operatorA(t). In this paper, we present a method, which is founded on linear multistep methods, which discretize a time-independent part of the operatorA(t) in an implicit way, and the other part in an explicit way. We study stability and convergence for this method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396412
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  • 10
    Electronic Resource
    Electronic Resource
    Mixed finite elements in ℝ3 (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 315-341 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present here some new families of non conforming finite elements in ℝ3. These two families of finite elements, built on tetrahedrons or on cubes are respectively conforming in the spacesH(curl) andH(div). We give some applications of these elements for the approximation of Maxwell's equations and equations of elasticity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396415
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