An Efficient EXCMG-Newton Method Combined with Fourth-Order Compact Schemes for Semilinear Poisson Equations
Year: 2023
Author: Pinxia Wu, Kejia Pan, Weiwei Ling, Dongdong He
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 1 : pp. 119–139
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.240222.210722
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 1 : pp. 119–139
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Semilinear Poisson equation fourth-order compact scheme EXCMG-Newton method high efficiency bi-quartic interpolation.