Library

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
  • ddc:000  (13)
  • 1
    facet.materialart.
    Unknown
    Multilevel Newton h-p Collocation (1994)
    Details
    Publication Date: 2014-02-26
    Description: We derive a simple accuracy matching strategy for inexact Gauss Newton methods and apply it to the numerical solution of boundary value problems of ordinary differential equations by collocation. The matching strategy is based on an affine contravariant convergence theorem, i. e. , the characteristic constants are invariant under affine transformations of the domain. The inexact Gauss Newton method is applied to an integral formulation of the BVP. As discretization for the arising linear subproblems we employ adaptive collocation at Gaussian nodes with varying local orders and stepsizes. The grids are chosen via adaptive refinement and order selection.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 2
    facet.materialart.
    Unknown
    Spirals in Scalar Reaction-Diffusion Equations (1995)
    Details
    Publication Date: 2014-02-26
    Description: Spiral-like patterns are an often observed phenomenon in chemical experiments such as the Belousov-Zhabotinskii reaction. The talk is concerned with a new PDE model whose solutions have the form of rotating spirals. In contrast to previous approaches it is based on a {\em scalar\/} reaction diffusion equation defined on a disk. A particular choice of boundary conditions leads to a non-selfadjoint operator which permits non-trivial dynamics. We study this equation using a combination of equivariant bifurcation theory and numerical simulations. The latter involves the direct simulation of the time dependent system as well as the computation of rotating waves and their stability.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 3
    facet.materialart.
    Unknown
    An Implementation of Extrapolation Codes in C++. (1993)
    Details
    Publication Date: 2014-02-26
    Description: This report describes the new object oriented implementation of extrapolation codes {\sc Eulex, Eulsim, Difex} for ordinary differential equations. The resulting C++ class library provides a simple and flexible interface to these methods and incorporates advanced features like continuous output and order-stepsize freezing. The interface of the ODE classes allows in particular a user-defined solver for the linear systems occuring in the linearly implicit discretization scheme. The library also provides some classes for numerical objects such as vectors and (full) matrices. Due to the underlying data-view concept it is possible to access substructures without copying. In addition, we included several utility classes such as a timer and a minimal command language that may be useful in other contexts, too.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 4
    facet.materialart.
    Unknown
    Inexact Gauss Newton Methods for Parameter Dependent Nonlinear Problems. (1993)
    Details
    Publication Date: 2014-02-27
    Description: A new approach to inexact Gauss Newton methods for the solution of underdetermined nonlinear problems is presented. It is based on a convergence theorem being invariant under affine transformations of the domain and results in an easily implementable accuracy matching strategy for the arising linear subproblems which guarantees the quadratic convergence. Thanks to the weak assumptions on the given nonlinear problem, the results provide a general framework for multilevel Newton and continuation methods. As an example, a new multilevel Newton h-p collocation method for boundary value problems of ordinary differential equations is developed. It combines the inexact Newton method with a linear collocation solver using adaptive refinement and variable orders. The performance of the resulting C++ class library {\sc Cocon} is demonstrated by some numerical examples including singular perturbed problems. In addition, the new method is applied to a realistic railway bogie model in which a branch of periodic solutions emanates from a branch of fixed points at a Hopf bifurcation.
    Keywords: ddc:000
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 5
    facet.materialart.
    Unknown
    Symbolic Exploitation of Symmetry in Numerical Path-following. (1990)
    Details
    Publication Date: 2014-02-26
    Description: Parameter-dependent systems of nonlinear equations with symmetry are treated by a combination of symbolic and numerical computations. In the symbolic part of the algorithm the complete analysis of the symmetry occurs, and it is here where symmetrical normal forms, symmetry reduced systems, and block diagonal Jacobians are computed. Given a particular problem, the symbolic algorithm can create and compute through the list of possible bifurcations thereby forming a so-called tree of decisions correlated to the different types of symmetry breaking bifurcation points. The remaining part of the algorithm deals with the numerical pathfollowing based on the implicit reparametrisation as suggested and worked out by Deuflhard/Fiedler/Kunkel. The symmetry preserving bifurcation points are computed using recently developed augmented systems incorporating the use of symmetry. {\bf Keywords:} pathfollowing, mixed symbolic-numeric algorithm, parameter-dependent, nonlinear systems, linear representations.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 6
    facet.materialart.
    Unknown
    An Adaptive Continuation Method for Implicitly Defined Surfaces. (1992)
    Details
    Publication Date: 2014-02-26
    Description: A new method for the numerical aproximation of an implicitly defined surface is presented. It is a generalization of the Euler- Gauss-Newton method for implicitly defined (one- parameter) curves to the case of (two-parameter) surfaces. The basic task in the more general case is an efficient combination of modern CAGD techniques (such as triangular Bernstein-Bzier patches and the nine parameter Hermite interpolant) and the rank deficient Gauss-Newton method.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 7
    facet.materialart.
    Unknown
    Object Oriented Design of Multilevel Newton and Continuation Methods. (1994)
    Details
    Publication Date: 2014-02-26
    Description: We present a set of C++ classes that realize an abstract inexact Gauss Newton method in combination with a continuation process for the solution of parameter dependent nonlinear problems. The object oriented approach allows the continuation of different types of solutions within the same framework. \\{\bf Abstract: }We present a set of C++ classes that realize an abstract inexact Gauss Newton method in combination with a continuation process for the solution of parameter dependent nonlinear problems. The object oriented approach allows the continuation of different types of solutions within the same framework.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 8
    facet.materialart.
    Unknown
    Numerical Continuation of Periodic Orbits with Symmetry. (1994)
    Details
    Publication Date: 2014-02-26
    Description: We consider periodic orbits of autonomous parameter dependent ODE's. Starting from a shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincar\'e-section we develop a pathfollowing algorithm for periodic solutions based on a tangential continuation method with implicit reparametrization. For ODE's equivariant w.r.t. a finite group we show that spatial as well as spatio-temporal symmetries of periodic orbits can be exploited within the (multiple) shooting context. We describe how turning points, period doubling bifurcations and Hopf points along the branch of periodic solutions can be handled. Furthermore equivariant Hopf points and generic secondary bifurcations of periodic orbits with $ Z_m$-symmetry are treated. We tested the code with standard examples, e.g., the period doubling cascade in the Lorenz equations. To show the efficiency of the described methods we also used the program for an application from electronics, a ring oscillator with $n $ inverters. In this example the exploitation of symmetry reduces the amount of work for the continuation of periodic orbits from ${\cal O}(n^2)$ to ${\cal O}(n)$
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 9
    facet.materialart.
    Unknown
    A Subdivision Algorithm for the Computation of Unstable Manifolds and Global Attractors (1995)
    Details
    Publication Date: 2014-02-26
    Description: Each invariant set of a given dynamical system is part of the global attractor. Therefore the global attractor contains all the potentially interesting dynamics, and, in particular, it contains every (global) unstable manifold. For this reason it is of interest to have an algorithm which allows to approximate the global attractor numerically. In this article we develop such an algorithm using a subdivision technique. We prove convergence of this method in a very general setting, and, moreover, we describe the qualitative convergence behavior in the presence of a hyperbolic structure. The algorithm can successfully be applied to dynamical systems of moderate dimension, and we illustrate this fact by several numerical examples.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 10
    facet.materialart.
    Unknown
    Einführung in die Numerische Mathematik. (1990)
    Details
    Publication Date: 2014-02-26
    Description: Diese Vorlesung ist eine Einführung in die Numerische Mathematik als einem der drei Bereiche (neben den Naturwissenschaften und der Informatik) des am besten mit dem Begriff Scientific Computing charakterisierten Forschungsgebietes. Aufgabe dieser relativ jungen Wissenschaft ist die Entwicklung von Rechenverfahren für Probleme aus den Naturwissenschaften mit Hilfe mathematischer Methoden.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...