TY - JOUR
T1 - An Efficient EXCMG-Newton Method Combined with Fourth-Order Compact Schemes for Semilinear Poisson Equations
AU - Wu , Pinxia
AU - Pan , Kejia
AU - Ling , Weiwei
AU - He , Dongdong
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 119
EP - 139
PY - 2023
DA - 2023/01
SN - 13
DO - http://doi.org/10.4208/eajam.240222.210722
UR - https://global-sci.org/intro/article_detail/eajam/21305.html
KW - Semilinear Poisson equation, fourth-order compact scheme, EXCMG-Newton method, high efficiency, bi-quartic interpolation.
AB - <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>