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Faster SDC convergence on non-equidistant grids by DIRK sweeps

Please always quote using this URN:urn:nbn:de:0296-matheon-12711
  • Spectral deferred correction methods for solving stiff ODEs are known to converge rapidly towards the collocation limit solution on equidistant grids, but show a much less favourable contraction on non-equidistant grids such as Radau-IIa points. We interprete SDC methods as fixed point iterations for the collocation system and propose new DIRK-type sweeps for stiff problems based on purely linear algebraic considerations. Good convergence is recovered also on non-equidistant grids. The properties of different variants are explored on a couple of numerical examples.

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Metadaten
Author:Martin Weiser
URN:urn:nbn:de:0296-matheon-12711
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2013/12/20
Release Date:2013/12/20
Tag:spectral deferred correction
Institute:Zuse Institute Berlin (ZIB)
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L06 Multistep, Runge-Kutta and extrapolation methods
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M70 Spectral, collocation and related methods
Preprint Number:1048
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