ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Articles  (19)
  • CR: 5.17  (19)
  • Springer  (19)
  • American Institute of Physics
  • Cell Press
  • Oxford University Press
  • 2005-2009
  • 1985-1989
  • 1975-1979  (19)
  • 1945-1949
  • 2010
  • 2007
  • 2006
  • 2005
  • 1978  (19)
  • 1945
  • Mathematics  (19)
  • Nature of Science, Research, Systems of Higher Education, Museum Science
  • Economics
  • Natural Sciences in General
  • Electrical Engineering, Measurement and Control Technology
Collection
  • Articles  (19)
Source
Keywords
Publisher
  • Springer  (19)
  • American Institute of Physics
  • Cell Press
  • Oxford University Press
Years
  • 2005-2009
  • 1985-1989
  • 1975-1979  (19)
  • 1945-1949
Year
Topic
  • Mathematics  (19)
  • Nature of Science, Research, Systems of Higher Education, Museum Science
  • Economics
  • Natural Sciences in General
  • Electrical Engineering, Measurement and Control Technology
  • 1
    Electronic Resource
    Electronic Resource
    Stability properties of variable stepsize variable formula methods (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 175-182 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397474
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    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
    Keywords: AMS (MOS): 65L05, 65M10, 65M15, 65M20, 65N15, 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398506
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Error estimates for the finite element solution of variational inequalities (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 1-16 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396010
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    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
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397472
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Efficient algorithms for solving tensor product finite element equations (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 49-61 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N20 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396013
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    On the order of composite multistep methods for ordinary differential equations (1978)
    Springer
    Numerische Mathematik 29 (1978), S. 381-396 
    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, a general class ofk-step methods for the numerical solution of ordinary differential equations is discussed. It is shown that methods with order of consistencyq have order of convergence (q+1) if a very simple condition is satisfied. This result gives a new aspect to previous results of Spijker; it also serves as a starting point for a new theory of cyclick-step methods, completing an approach of Donelson and Hansen. It facilitates the practical determination of high-order cyclick-step methods, especially of stiffly stable,k-step methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01432876
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    On the order of iterated defect correction (1978)
    Springer
    Numerische Mathematik 29 (1978), S. 409-424 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65LO5 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In a recent article [2] Frank and Überhuber define and motivate the method of iterated defect correction for Runge-Kutta methods. They prove a theorem on the order of that method using the theory of asymptotic expansions. In this paper we give similar results using the theory of Butcher series (see [4]). Our proofs are purely algebraic. We don't restrict our considerations to Runge-Kutta methods, but we admit arbitrary linear one-step methods. At the same time we consider more general defect functions as in [2].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01432878
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Zur Stabilität von Differenzenverfahren für Systeme linearer gewöhnlicher Randwertaufgaben (1978)
    Springer
    Numerische Mathematik 29 (1978), S. 209-226 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L 10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we give a simple stability theory for finite difference approximations to linear ordinary boundary value problems. In particular we consider stability with respect to a maximum norm including all difference quotients up to the order of the differential equation. It is shown that stability in this sense holds if and only if the principal part of the differential equation is discretized in a “stable way”. This last property is characterized by root conditions which we prove to be satisfied for some classes of finite difference schemes. Our approach simplifies and generalizes some known results of the literature where Sobolev norms or merely the maximum norm are used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390339
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    Transformation of three-dimensional regions onto rectangular regions by elliptic systems (1978)
    Springer
    Numerische Mathematik 29 (1978), S. 397-407 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 31-04, 65N05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A transformation method is developed which may be used to solve various types of boundary value problems on three-dimensional regions with an arbitrary boundary. The implementation of the method is illustrated in the solution of a potential flow problem. All computations are performed on a cubic mesh in a rectangular region.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01432877
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    The defect correction principle and discretization methods (1978)
    Springer
    Numerische Mathematik 29 (1978), S. 425-443 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65J05, 65L99 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Recently, a number of closely related techniques for error estimation and iterative improvement in discretization algorithms have been proposed. In this article, we expose the common structural principle of all these techniques and exhibit the principal modes of its implementation in a discretization context.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01432879
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 11
    Electronic Resource
    Electronic Resource
    Einschließungsaussagen bei Differentialoperatoren zweiter Ordnung durch punktweise Ungleichungen (1978)
    Springer
    Numerische Mathematik 30 (1978), S. 93-101 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider non-inverse positive differential operators of the second order and show that error estimates can be obtained through methods of inverse positivity alone. This means a significant simplification if the operator has only one negative eigenvalue. In addition we show how to obtain Range-Domain implications for operators with mixed boundary conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01403909
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 12
    Electronic Resource
    Electronic Resource
    A Taylor series method for the numerical solution of two-point boundary value problems (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 359-375 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For the numerical solution of two-point boundary value problems a shooting algorithm based on a Taylor series method is developed. Series coefficients are generated automatically by recurrence formulas. The performance of the algorithm is demonstrated by solving six problems arising in nonlinear shell theory, chemistry and superconductivity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01404566
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 13
    Electronic Resource
    Electronic Resource
    Extrapolation methods for dynamic partial differential equations (1978)
    Springer
    Numerische Mathematik 29 (1978), S. 269-285 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65 M 99 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Several extrapolation procedures are presented for increasing the order of accuracy in time for evolutionary partial differential equations. These formulas are based on finite difference schemes in both the spatial and temporal directions. One of these schemes reduces to a Runge-Kutta type formula when the equations are linear. On practical grounds the methods are restricted to schemes that are fourth order in time and either second, fourth or sixth order in space. For hyperbolic problems the second order in space methods are not useful while the fourth order methods offer no advantage over the Kreiss-Oliger method unless very fine meshes are used. Advantages are first achieved using sixth order methods in space coupled with fourth order accuracy in time. The averaging procedure advocated by Gragg does not increase the efficiency of the scheme. For parabolic problems severe stability restrictions are encountered that limit the applicability to problems with large cell Reynolds number. Computational results are presented confirming the analytic discussions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389212
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 14
    Electronic Resource
    Electronic Resource
    The method of lines for Poisson's equation with nonlinear or free boundary conditions (1978)
    Springer
    Numerische Mathematik 29 (1978), S. 329-344 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65M20 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The method of lines is used to solve Poisson's equation on an irregular domain with nonlinear or free boundary conditions. The partial differential equation is approximated by a system of second order ordinary differential equations subject to multi-point boundary conditions. The system is solved with an SOR iteration which employs invariant imbedding for each one dimensional problem. An application of the method to a boundary control problem and to a free surface problem arising in electrochemical machining is described. Finally, some theoretical convergence results are presented for a model problem with radiative boundary conditions on fixed boundaries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389216
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 15
    Electronic Resource
    Electronic Resource
    High order methods for the numerical integration of ordinary differential equations (1978)
    Springer
    Numerische Mathematik 30 (1978), S. 385-409 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary High order implicit integration formulae with a large region of absolute stability are developed for the approximate numerical integration of both stiff and non-stiff systems of ordinary differential equations. The algorithms derived behave essentially like one step methods and are demonstrated by direct application to certain particular examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398507
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 16
    Electronic Resource
    Electronic Resource
    Higher order methods for a singularly perturbed problem (1978)
    Springer
    Numerische Mathematik 30 (1978), S. 267-279 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A finite element method using piecewise polynomials of degree ≦k is used to approximate the problem εu″+u′=f, ε〉0 a small parameter. A very irregular mesh is used. On this mesh error estimates of order0(h k+1) are obtained uniformly in ε,h the maximum stepsize, fork≧2. The condition number of the system of linear equations one has to solve in order to get the approximation is estimated. Extension of the results to more complicated problems is briefly indicated. Finally, a numerical example is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01411843
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 17
    Electronic Resource
    Electronic Resource
    On the stability properties of Brown's multistep multiderivative methods (1978)
    Springer
    Numerische Mathematik 30 (1978), S. 25-38 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Brown introducedk-step methods usingl derivatives. We investigate for whichk andl the methods are stable or unstable. It is seen that to anyl the method becomes unstable fork large enough. All methods withk≦2(l+1) are stable. Fork=1,2,..., 18 there exists aλ k such that the methods are stable for anyl ≧λ k and unstable for anyl 〈λ k . Theλ k are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01403904
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 18
    Electronic Resource
    Electronic Resource
    Some equilibrium finite element methods for two-dimensional elasticity problems (1978)
    Springer
    Numerische Mathematik 30 (1978), S. 103-116 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider some equilibrium finite element methods for two-dimensional elasticity problems. The stresses and the displacements are approximated by using piecewise linear functions. We establishL 2-estimates of orderO(h 2) for both stresses and displacements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01403910
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 19
    Electronic Resource
    Electronic Resource
    Liapunov functions and error bounds for approximate solutions of ordinary differential equations (1978)
    Springer
    Numerische Mathematik 30 (1978), S. 411-414 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L99 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It is shown that Liapunov functions may be used to obtain error bounds for approximate solutions of systems of ordinary differential equations. These error bounds may reflect the behaviour of the error more accurately than other bounds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398508
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...