A Class of A Stable Summation by Parts Time Integration Schemes

This repository contains some code used in the article

@article{ranocha2021class,
  title={A New Class of {$A$} Stable Summation by Parts Time Integration Schemes
         with Strong Initial Conditions},
  author={Ranocha, Hendrik and Nordstr{\"o}m, Jan},
  journal={Journal of Scientific Computing},
  year={2021},
  month={03},
  volume={87},
  doi={10.1007/s10915-021-01454-7},
  eprint={2003.03889},
  eprinttype={arxiv},
  eprintclass={math.NA}
}

Since integration by parts is an important tool when deriving energy or entropy estimates for differential equations, one may conjecture that some form of summation by parts (SBP) property is necessarily involved in provably stable numerical methods. This article contributes to this topic by proposing a novel class of A stable SBP time integration methods including the classical Lobatto IIIA collocation method, not previously formulated as an SBP scheme. Additionally, a related SBP scheme including the classical Lobatto IIIB collocation method is developed.

If you find these results useful, please cite the article mentioned above. If you use the implementations provided here, please cite this repository as

@misc{ranocha2020classRepro,
  title={{SBP-projection-in-time-notebooks}.
         {A} Class of {$A$} Stable Summation by Parts
         Time Integration Schemes},
  author={Ranocha, Hendrik and Nordstr{\"o}m, Jan},
  year={2020},
  month={03},
  howpublished={\url{https://github.com/ranocha/SBP-projection-in-time-notebooks}},
  doi={10.5281/zenodo.3699173}
}

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