@Article{JCM-36-542, author = {Jiang , Yaolin and Miao , Zhen}, title = {Quasi-Newton Waveform Relaxation Based on Energy Method}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {4}, pages = {542--562}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1702-m2016-0700}, url = {http://global-sci.org/intro/article_detail/jcm/12304.html} }