TY - JOUR T1 - Quasi-Newton Waveform Relaxation Based on Energy Method AU - Jiang , Yaolin AU - Miao , Zhen JO - Journal of Computational Mathematics VL - 4 SP - 542 EP - 562 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1702-m2016-0700 UR - https://global-sci.org/intro/article_detail/jcm/12304.html KW - Waveform relaxation, quasi-Newton, Energy method, Superlinear, Parallelism. AB -
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. Finally several parallel numerical experiments are implemented to confirm the effectiveness of the above theories.