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