Faster SDC convergence on non-equidistant grids by DIRK sweeps

  • 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 WeiserORCiD
Document Type:Article
Parent Title (German):BIT Numerical Mathematics
Volume:55
Issue:4
First Page:1219
Last Page:1241
Year of first publication:2015
Pagenumber:22
Preprint:urn:nbn:de:0297-zib-18662
DOI:https://doi.org/10.1007/s10543-014-0540-y