Quasi-Newton Waveform Relaxation Based on Energy Method

@article{Miao2018QuasiNewtonWR,
  title={Quasi-Newton Waveform Relaxation Based on Energy Method},
  author={Yao Miao},
  journal={Journal of Computational Mathematics},
  year={2018}
}
  • Y. Miao
  • Published 1 June 2018
  • Mathematics
  • Journal of Computational Mathematics
A quasi-Newton waveform relaxation (WR) algorithm for semi-linear reaction-diffusion equations is presented at first in this paper. Using the idea of energy estimate, a general proof method for convergence of the continuous case and the discrete case of quasi-Newton WR is given, which appears to be the superlinear rate. The semi-linear wave equation and semi-linear coupled equations can similarly be solved by quasi-Newton WR algorithm and be proved as convergent with the energy inequalities… 

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