(untitled) (CSIAM Transactions on Applied Mathematics, 2023)
The aim of this paper is to analyze the robust convergence of a class of parareal algorithms for solving parabolic problems. The coarse propagator is fixed to the backward Euler method and the fine propagator is a high-order single step integrator. Under some conditions on the fine propagator, we show that there exists some critical J_∗ such that the parareal solver converges linearly with a convergence rate near 0.3, provided that the ratio between the coarse time step and fine time step named J satisfies J ≥ J_∗. The convergence is robust even if the problem data is nonsmooth and incompatible with boundary conditions. The qualified methods include all absolutely stable single step methods, whose stability function satisfies |r(−∞)|