Difference approximations for initial boundary-value problems

@article{Kreiss1971DifferenceAF,
  title={Difference approximations for initial boundary-value problems},
  author={H. O. Kreiss},
  journal={Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences},
  year={1971},
  volume={323},
  pages={255 - 261}
}
The problem of the stability of difference approximations for initial boundary-value problems is examined and recent results obtained in this field by Gustafsson, Kreiss & Sundstrom (1971) are presented. It is shown that even for scalar equations the Ryabenkii-Godunow condition is not sufficient for stability and a procedure is outlined which leads to a slightly strengthened form of this condition which is satisfactory in practice.