Convergence rates for adaptive approximation of ordinary differential equations

@article{Moon2003ConvergenceRF,
  title={Convergence rates for adaptive approximation of ordinary differential equations},
  author={Kyoung-Sook Moon and Anders Szepessy and Ra{\'u}l Tempone and Georgios E. Zouraris},
  journal={Numerische Mathematik},
  year={2003},
  volume={96},
  pages={99-129}
}
This paper constructs an adaptive algorithm for ordinary differential equations and analyzes its asymptotic behavior as the error tolerance parameter tends to zero. An adaptive algorithm, based on the error indicators and successive subdivision of time steps, is proven to stop with the optimal number, N , of steps up to a problem independent factor defined in the algorithm. A version of the algorithm with decreasing tolerance also stops with the total number of steps, including all refinement… CONTINUE READING
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