Stability and boundedness in the numerical solution of initial value problems

@article{Spijker2017StabilityAB,
  title={Stability and boundedness in the numerical solution of initial value problems},
  author={Marc Nico Spijker},
  journal={Math. Comput.},
  year={2017},
  volume={86},
  pages={2777-2798}
}
Abstract. This paper concerns the theoretical analysis of step-by-step meth-ods for solving initial value problems in ordinary and partial differential equa-tions.The main theorem of the paper answers a natural question arising in thelinear stability analysis of such methods. It guarantees a (strong) version ofnumerical stability—under a stepsize restriction related to the stability regionof the numerical method and to a circle condition on the differential equation.The theorem also settles an… 
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