On the zero-stability of multistep methods on smooth nonuniform grids

@article{Sderlind2018OnTZ,
  title={On the zero-stability of multistep methods on smooth nonuniform grids},
  author={Gustaf S{\"o}derlind and Imre Fekete and Istv{\'a}n Farag{\'o}},
  journal={BIT Numerical Mathematics},
  year={2018},
  volume={58},
  pages={1125-1143}
}
  • Gustaf Söderlind, Imre Fekete, István Faragó
  • Published 2018
  • Mathematics
  • BIT Numerical Mathematics
  • In order to be convergent, linear multistep methods must be zero stable. While constant step size theory was established in the 1950’s, zero stability on nonuniform grids is less well understood. Here we investigate zero stability on compact intervals and smooth nonuniform grids. In practical computations, step size control can be implemented using smooth (small) step size changes. The resulting grid $$\{t_n\}_{n=0}^N$${tn}n=0N can be modeled as the image of an equidistant grid under a smooth… CONTINUE READING

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