Predictor-corrector domain decomposition algorithm for parabolic problems on graphs (Q2891960)

The authors present a parallel predictor-corrector type algorithm for solving linear one-dimensional parabolic problems on graphs. By using energy estimates it is proved that the predictor-corrector algorithm is unconditionally stable. The relation between space and time steps is still required in order to get convergence of the discrete solution, since only a conditional approximation is obtained due to the truncation error introduced at the prediction step. Applying results of \textit{P. Vabishchevich} [Comput. Methods Appl. Math. 11, No. 2, 241--268 (2011)] and using the equivalence of the predictor corrector scheme and the Douglas type scheme, one gets new convergence estimates. The asymptotic optimality of different theoretical accuracy estimates is compared with results of computational experiments.