Operator splittings and spatial approximations for evolution equations

@article{Btkai2009OperatorSA,
  title={Operator splittings and spatial approximations for evolution equations},
  author={Andr{\'a}s B{\'a}tkai and Petra Csom{\'o}s and Gregor Nickel},
  journal={Journal of Evolution Equations},
  year={2009},
  volume={9},
  pages={613-636}
}
The convergence of various operator splitting procedures, such as the sequential, the Strang and the weighted splitting, is investigated in the presence of a spatial approximation. To this end the relevant notions and results of numerical analysis are presented, a variant of Chernoff’s product formula is proved and the general Trotter–Kato approximation theorem is used. The methods are applied to an abstract partial delay differential equation. 
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