The SBP-SAT technique for initial value problems

作者：Lundquist Tomas^*; Nordstrom Jan

来源：Journal of Computational Physics, 2014, 270: 86-104.

DOI：10.1016/j.jcp.2014.03.048

• Time integration
• Initial value problems
• High order accuracy
• Initial boundary value problems
• Boundary conditions
• Global methods
• Stability
• Convergence
• Summation-by-parts operators
• Stiff problems

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.

• 出版日期2014-8-1