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  • Articles  (247)
  • Immunocytochemistry  (149)
  • CR: 5.17  (98)
  • Springer  (247)
  • 1980-1984  (247)
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  • Articles  (247)
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  • 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
    Behandlung steifer Anfangswertprobleme gewöhnlicher Differentialgleichungen mit adaptiven Runge-Kutta-Methoden (1982)
    Springer
    Computing 29 (1982), S. 153-165 
    Details
    ISSN: 1436-5057
    Keywords: 65L05 ; CR: 5.17 ; Numer. Analysis ; verallgemeinerte Runge-Kutta-Methoden ; steife Probleme
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract Adaptive Runge-Kutta-methods are considered. Investigations of stability for these linear implicit methods are studied. For the application a LS-stable method of order four with an adaptive stepsize control is proposed. Test results for 25 stiff initial value problems for different tolerances are discussed.
    Notes: Zusammenfassung Es werden adaptive Runge-Kutta-Verfahren betrachtet und Stabilitätsuntersuchungen für diese linear impliziten Methoden durchgeführt. Für die Anwendung wird ein LS-stabiles Verfahren vierter Ordnung mit einer angepaßten Schrittweitenkontrolle vorgeschlagen. Testergebnisse von 25 stiff Anfangswertproblemen für verschiedenen Toleranzen werden diskutiert.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02249938
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  • 3
    Electronic Resource
    Electronic Resource
    Approximation of time-dependent free boundaries (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 179-199 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; Primary 65N30 ; Secondary 35R35 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Two problems are considered in the paper: the first of them is connected with elliptic variational inequalities and consists in developing a moving obstacle algorithm for approximating the unknown free boundary; the other problem is linked with numerical solution of the Stefan problem, which is formulated in the similar way as in the elliptic case. Some computational aspects are also discussed in the paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400538
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  • 4
    Electronic Resource
    Electronic Resource
    Finite elements for parabolic equations backwards in time (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 207-227 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65M30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Several regularization methods for parabolic equations backwards in time together with the usual additional constraints for their solution are considered. The error of the regularization is estimated from above and below. For a “boundary value problem in time”-method, finite elements as well as a time discretization are introduced and the error with respect to the regularized solution is estimated, thus giving an overall error of the discrete regularized problem. The algorithm is tested in simple numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400540
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  • 5
    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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  • 6
    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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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Adams methods for neutral functional differential equations (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 221-230 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper Adams type methods for the special case of neutral functional differential equations are examined. It is shown thatk-step methods maintain orderk+1 for sufficiently small step size in a sufficiently smooth situation. However, when these methods are applied to an equation with a “non-smooth” solution the order of convergence is only one. Some computational considerations are given and numerical experiments are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01408695
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  • 9
    Electronic Resource
    Electronic Resource
    Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approximations (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 309-324 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A method for improvement of the numerical solution of differential equations by incorporation of asymptotic approximations is investigated for a class of singular perturbation problems. Uniform error estimates are derived for this method when implemented in known difference schemes and applied to linear second order O.D.E.'s. An improvement by a factor ofε n+1 can be obtained (where ɛ is the “small” parameter andn is the order of the asymptotic approximation) for a small amount of extra work. Numerical experiments are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01407865
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  • 10
    Electronic Resource
    Electronic Resource
    Finite difference methods and their convergence for a class of singular two point boundary value problems (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 341-350 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We discuss the construction of three-point finite difference approximations and their convergence for the class of singular two-point boundary value problems: (x α y′)′=f(x,y), y(0)=A, y(1)=B, 0〈α〈1. We first establish a certain identity, based on general (non-uniform) mesh, from which various methods can be derived. To obtain a method having order two for all α∈(0,1), we investigate three possibilities. By employing an appropriate non-uniform mesh over [0,1], we obtain a methodM 1 based on just one evaluation off. For uniform mesh we obtain two methodsM 2 andM 3 each based on three evaluations off. For α=0,M 1 andM 2 both reduce to the classical second-order method based on one evaluation off. These three methods are investigated, theirO(h 2)-convergence established and illustrated by numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01407867
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