@Article{EAJAM-13-1,
author = {Wu, Pinxia and Pan, Kejia and Weiwei, Ling and He, Dongdong},
title = {An Efficient EXCMG-Newton Method Combined with Fourth-Order Compact Schemes for Semilinear Poisson Equations},
journal = {East Asian Journal on Applied Mathematics},
year = {2023},
volume = {13},
number = {1},
pages = {119--139},
abstract = {<p style="text-align: justify;">A fast solver for nonlinear systems arising from fourth-order compact finite
difference schemes for two-dimensional semilinear Poisson equations is constructed. Applying the extrapolation and bi-quartic interpolation to two numerical solutions from the
previous two levels of grids, we determine a suitable initial guess for the Newton iterations on the next finer grid. It is fifth-order accurate, which substantially reduces the
number of Newton iterations required. Moreover, an extrapolated solution of sixth-order
accuracy can be easily constructed on the whole fine grid. Numerical results suggest that
the method is much more efficient than the existing multigrid methods for semilinear
problems.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.240222.210722},
url = {https://global-sci.com/article/82411/an-efficient-excmg-newton-method-combined-with-fourth-order-compact-schemes-for-semilinear-poisson-equations}
}