Abstract
A detailed account of the stability and accuracy properties of the SBP-SAT technique for numerical time integration is presented. We show how the technique can be used to formulate both global and multi-stage methods with high order of accuracy for both stiff and non-stiff problems. Linear and non-linear stability results, including A-stability, L-stability and B-stability are proven using the energy method for general initial value problems. Numerical experiments corroborate the theoretical properties.
| Original language | English |
|---|---|
| Pages (from-to) | 86-104 |
| Number of pages | 19 |
| Journal | Journal of Computational Physics |
| Volume | 270 |
| DOIs | |
| Publication status | Published - 1 Aug 2014 |
| Externally published | Yes |
Keywords
- Boundary conditions
- Convergence
- Global methods
- High order accuracy
- Initial boundary value problems
- Initial value problems
- Stability
- Stiff problems
- Summation-by-parts operators
- Time integration
ASJC Scopus subject areas
- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics