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Numerical Algorithms

, Volume 41, Issue 2, pp 103–126 | Cite as

Analysis of a defect correction method for geometric integrators

  • Harald HofstätterEmail author
  • Othmar Koch
Article

We discuss a new variant of Iterated Defect Correction (IDeC), which increases the range of applicability of the method. Splitting methods are utilized in conjunction with special integration methods for Hamiltonian systems, or other initial value problems for ordinary differential equations with a particular structure, to solve the neighboring problems occurring in the course of the IDeC iteration. We demonstrate that this acceleration technique serves to rapidly increase the convergence order of the resulting numerical approximations, up to the theoretical limit given by the order of certain superconvergent collocation methods.

Keywords

composition methods geometric integration Hamiltonian systems iterated defect correction splitting methods 

AMS subject classification

65L05 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyViennaAustria

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