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  • Artikel  (45)
  • CR: 5.17  (45)
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  • Springer  (45)
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  • Mathematik  (45)
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  • 1
    Digitale Medien
    Digitale Medien
    Stability properties of variable stepsize variable formula methods (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 175-182 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65 L05 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary When variable stepsize variable formula methods (VSVFM's) are used in the solution of systems of first order differential equations instability arises sometimes. Therefore it is important to find VSVFM's whose zerostability properties are not affected by the choice of both the stepsize and the formula. The Adams VSVFM's are such methods. In this work a more general class of methods which contains the Adams VSVFM's is discussed and it is proved that the zero-stability of the class is not affected by the choice of the stepsize and of the formula.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01397474
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    A-priori error estimates of Galerkin backward differentiation methods in time-inhomogeneous parabolic problems (1978)
    Springer
    Numerische Mathematik 30 (1978), S. 369-383 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65L05, 65M10, 65M15, 65M20, 65N15, 65N30 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Backward differentiation methods up to orderk=5 are applied to solve linear ordinary and partial (parabolic) differential equations where in the second case the space variables are discretized by Galerkin procedures. Using a mean square norm over all considered time levels a-priori error estimates are derived. The emphasis of the results lies on the fact that the obtained error bounds do not depend on a Lipschitz constant and the dimension of the basic system of ordinary differential equations even though this system is allowed to have time-varying coefficients. It is therefore possible to use the bounds to estimate the error of systems with arbitrary varying dimension as they arise in the finite element regression of parabolic problems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01398506
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  • 3
    Digitale Medien
    Digitale Medien
    Error estimates for the finite element solution of variational inequalities (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 1-16 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We study the mixed finite element approximation of variational inequalities, taking as model problems the so called “obstacle problem” and “unilateral problem”. Optimal error bounds are obtained in both cases.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396010
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  • 4
    Digitale Medien
    Digitale Medien
    One-step methods of any order for ordinary differential equations with discontinuous right-hand sides (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 131-152 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65L05 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The right-hand sides of a system of ordinary differential equations may be discontinuous on a certain surface. If a trajectory crossing this surface shall be computed by a one-step method, then a particular numerical analysis is necessary in a neighbourhood of the point of intersection. Such an analysis is presented in this paper. It shows that one can obtain any desired order of convergence if the method has an adequate order of consistency. Moreover, an asymptotic error theory is developed to justify Richardson extrapolation. A general one-step method is constructed satisfying the conditions of the preceding theory. Finally, a simplified Newton iteration scheme is used to implement this method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01397472
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  • 5
    Digitale Medien
    Digitale Medien
    Splineapproximationen von beliebigem Defekt zur numerischen Lösung gewöhnlicher Differentialgleichungen. Teil I (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 147-157 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS) ; 65L65 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In 1967, F.R. Loscalzo und T.D. Talbot presented a procedure for obtaining polynomial spline approximations of defect one for solutions of the initial value problem for first order ordinary differential equations. This method is generalized and investigated for spline approximations of arbitrary defect. The results are analogous to those of the defect one. In the first part of this paper the divergence problem is treated. The convergent procedures are investigated in a following second part of this paper.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01404871
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  • 6
    Digitale Medien
    Digitale Medien
    Sur les elements finis rationnels de Wachspress (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 247-270 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65D05, 65N30, 41A20 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Beschreibung / Inhaltsverzeichnis: Résumé Ce travail est consacré à l'étude d'éléments finis rationnels de Wachspress (cf. [15]) sur un quadrilatère. Après avoir étudié la construction et les propriétés de ces éléments finis, on obtient une évaluation de l'erreur d'interpolation correspondante.
    Notizen: Summary This paper is devoted to the study of Wachspress's rational finite elements (cf. [15]) over a quadrilateral. After studying construction and properties of these finite elements, we get an estimate of the corresponding interpolation error.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01397000
    Standort Signatur Erwartet Verfügbarkeit
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  • 7
    Digitale Medien
    Digitale Medien
    Splineapproximationen von beliebigem Defekt zur numerischen Lösung gewöhnlicher Differentialgleichungen. Teil II (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 343-358 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65L65 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In the first part [5] a general procedure is presented to obtain polynomial spline approximations of arbitrary defect for the solution of the initial value problem of ordinary differential equations. The essential result is a divergence theorem in dependence of the polynomial degree and the defect of the spline functions. In this second part the convergent procedures are investigated and two convergence theorems are proved. Furthermore the question is treated, whether the convergent procedures are appropriate for the numerical solution of stiff equations. The paper is finished by a convergence theorem for a procedure producing spline approximations in a natural way by the discrete approximations of an arbitrary difference method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01397006
    Standort Signatur Erwartet Verfügbarkeit
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  • 8
    Digitale Medien
    Digitale Medien
    Efficient algorithms for solving tensor product finite element equations (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 49-61 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65N20 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary There are currently several highly efficient methods for solving linear systems associated with finite difference approximations of Poisson's equation in rectangular regions. These techniques are employed to develop both direct and iterative methods for solving the linear systems arising from the use ofC 0 quadratic orC 1 cubic tensor product finite elements.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396013
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  • 9
    Digitale Medien
    Digitale Medien
    Acceleration of convergence for finite element solutions of the Poisson equation (1979)
    Springer
    Numerische Mathematik 33 (1979), S. 43-53 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS (Mos): 65N30 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Letu h be the finite element solution to−Δu=f with zero boundary conditions in a convex polyhedral domain Ω. Fromu h we calculate for eachz∈Ω and |α|≦1 an approximationu h −α (z) toD α u(z) with |D α u(z)−u h −α (z)|=O(h 2k−2) wherek is the order of the finite elements. The same superconvergence order estimates are obtained also for the boundary flux. We need not work on a regular mesh but we have to compute averages ofu h where the diameter of the domain of integration must not depend onh.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396494
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  • 10
    Digitale Medien
    Digitale Medien
    Extrapolation to the limit for numerical solutions of hyperbolic equations (1977)
    Springer
    Numerische Mathematik 28 (1977), S. 455-474 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65B05, 65M25, 65M99 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The application of extrapolation to the limit requires the existence of an asymptotic expansion in powers of the step size. In this paper one-and multi-step methods for the solution of hyperbolic systems of first order are considered. Conditions are formulated that ensure the asymptotic expansion. Methods of characteristics for quasilinear systems with two independent variables are included in this presentation. If a rectangular grid is used, also non-quasilinear systems are admissible. The main part of this paper deals with initial value problems. But it is shown that in some exceptional cases asymptotic expansions hold for initial-boundary problems, too.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01404347
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