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  • Articles  (97)
  • Other Sources
  • CR: 5.17  (97)
  • 1985-1989  (1)
  • 1980-1984  (96)
  • Mathematics  (97)
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  • Articles  (97)
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  • 1
    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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  • 2
    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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  • 3
    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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  • 4
    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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  • 5
    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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  • 6
    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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  • 7
    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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  • 8
    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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  • 9
    Electronic Resource
    Electronic Resource
    On the numerical analysis of the Von Karman equations: Mixed finite element approximation and continuation techniques (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 371-404 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The purpose of this paper is to study the approximation of the Von Karman equations by the mixed finite element scheme of Miyoshi and to follow the solutions arcs at a neighbourhood of the first eigenvalue of the linearized problem. This last problem is solved by a continuation method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01407870
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  • 10
    Electronic Resource
    Electronic Resource
    Maximale Konvergenzordnung bei der numerischen Lösung von Anfangswertproblemen mit Splines (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 449-463 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L65 ; CR: 5.17 ; AMS (MOS): 65L65 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary In [10] a general procedureV is presented to obtain spline approximations by collocation for the solutions of initial value problems for first order ordinary differential equations. In this paper the attainable order of convergence with respect to the maximum norm is characterized in dependence of the parameters involved inV; in particular the appropriate choice of the collocation points is considered.
    Notes: Zusammenfassung In [10] ist ein allgemeines VerfahrenV beschrieben, das die Lösungen von Anfangswertproblemen bei gewöhnlichen Differentialgleichungen erster Ordnung durch Splines approximiert. Die Konstruktion der Splines erfolgt hierbei mittels Kollokation. In dieser Arbeit wird die maximal erreichbare Konvergenzordnung vonV bezüglich der Maximumnorm in Abhängigkeit aller Parameter vonV charakterisiert, insbesondere wird auf die geeignete Wahl der Kollokationsknoten eingegangen.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01407875
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