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Inexact Gauss Newton Methods for Parameter Dependent Nonlinear Problems.

Please always quote using this URN: urn:nbn:de:0297-zib-5049
  • 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.

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Metadaten
Author:Andreas Hohmann
Document Type:Doctoral Thesis
Date of first Publication:1993/12/13
Series (Serial Number):ZIB-Report (TR-93-13)
ZIB-Reportnumber:TR-93-13
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