Analysis of a defect correction method for geometric integrators |
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Authors: | Harald Hofstätter Othmar Koch |
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Institution: | (1) Institute for Analysis and Scientific Computing, Vienna University of Technology, Vienna, Austria |
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Abstract: | 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.
This project was supported by the Special Research Program SFB F011 ‘AURORA’ of the Austrian Science Fund FWF. |
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Keywords: | composition methods geometric integration Hamiltonian systems iterated defect correction splitting methods |
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