Abstract
We investigate the Chebyshev spectral collocation and waveform relaxation methods for nonlinear conservation laws. Waveform relaxation methods allow to replace the system of nonlinear differential equations resulting from the application of spectral collocation methods by a sequence of linear problems which can be effectively integrated by highly stable implicit methods. The obtained numerical solution is then enhanced on the intervals of smoothness by the Gegenbauer reconstruction. The effectiveness of this approach is illustrated by numerical experiments.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 51-71 |
| Number of pages | 21 |
| Journal | Computational Methods in Applied Mathematics |
| Volume | 5 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2005 |
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Keywords
- Gegenbauer Reconstruction
- Nonlinear Conservation Law
- Pseudospectral Methods
- Waveform Relaxation Iterations
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics
Cite this
Spectral Collocation and Waveform Relaxation Methods with Gegenbauer Geconstruction for Nonlinear Conservation Laws. / Jackiewicz, Zdzislaw; Zubik-Kowal, B.
In: Computational Methods in Applied Mathematics, Vol. 5, No. 1, 2005, p. 51-71.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Spectral Collocation and Waveform Relaxation Methods with Gegenbauer Geconstruction for Nonlinear Conservation Laws
AU - Jackiewicz, Zdzislaw
AU - Zubik-Kowal, B.
PY - 2005
Y1 - 2005
N2 - We investigate the Chebyshev spectral collocation and waveform relaxation methods for nonlinear conservation laws. Waveform relaxation methods allow to replace the system of nonlinear differential equations resulting from the application of spectral collocation methods by a sequence of linear problems which can be effectively integrated by highly stable implicit methods. The obtained numerical solution is then enhanced on the intervals of smoothness by the Gegenbauer reconstruction. The effectiveness of this approach is illustrated by numerical experiments.
AB - We investigate the Chebyshev spectral collocation and waveform relaxation methods for nonlinear conservation laws. Waveform relaxation methods allow to replace the system of nonlinear differential equations resulting from the application of spectral collocation methods by a sequence of linear problems which can be effectively integrated by highly stable implicit methods. The obtained numerical solution is then enhanced on the intervals of smoothness by the Gegenbauer reconstruction. The effectiveness of this approach is illustrated by numerical experiments.
KW - Gegenbauer Reconstruction
KW - Nonlinear Conservation Law
KW - Pseudospectral Methods
KW - Waveform Relaxation Iterations
UR - http://www.scopus.com/inward/record.url?scp=33646544866&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33646544866&partnerID=8YFLogxK
U2 - 10.2478/cmam-2005-0002
DO - 10.2478/cmam-2005-0002
M3 - Article
AN - SCOPUS:33646544866
VL - 5
SP - 51
EP - 71
JO - Computational Methods in Applied Mathematics
JF - Computational Methods in Applied Mathematics
SN - 1609-4840
IS - 1
ER -