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.
Author: | Martin Weiser |
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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 |