A parareal approach of semi‐linear parabolic equations based on general waveform relaxation

  title={A parareal approach of semi‐linear parabolic equations based on general waveform relaxation},
  author={Jun Li and Yaolin Jiang and Zhen Miao},
  journal={Numerical Methods for Partial Differential Equations},
  pages={2017 - 2043}
We present a parareal approach of semi‐linear parabolic equations based on general waveform relaxation (WR) at the partial differential equation (PDE) level. An algorithm for initial‐boundary value problem and two algorithms for time‐periodic boundary value problem are constructed. The convergence analysis of three algorithms are provided. The results show that the algorithm for initial‐boundary value problem is superlinearly convergent while both algorithms for the time‐periodic boundary value… 

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