Quasi-Newton Waveform Relaxation Based on Energy Method (Journal of Computational Mathematics, 2018)
A quasi-Newton waveform relaxation (WR) algorithm for semi-linear reaction-diffusionequations is presented at first in this paper. Using the idea of energy estimate, a generalproof method for convergence of the continuous case and the discrete case of quasi-NewtonWR is given, which appears to be the superlinear rate. The semi-linear wave equation andsemi-linear coupled equations can similarly be solved by quasi-Newton WR algorithm andbe proved as convergent with the energy inequalities. Finally several parallel numericalexperiments are implemented to confirm the effectiveness of the above theories.