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Volume 13, Issue 1
An Efficient EXCMG-Newton Method Combined with Fourth-Order Compact Schemes for Semilinear Poisson Equations

Pinxia Wu, Kejia Pan, Weiwei Ling & Dongdong He

East Asian J. Appl. Math., 13 (2023), pp. 119-139.

Published online: 2023-01

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  • 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.

  • AMS Subject Headings

65N06, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-13-119, author = {Wu , PinxiaPan , KejiaLing , Weiwei 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 = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.240222.210722}, url = {http://global-sci.org/intro/article_detail/eajam/21305.html} }
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 -

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.

Wu , PinxiaPan , KejiaLing , Weiwei and He , Dongdong. (2023). An Efficient EXCMG-Newton Method Combined with Fourth-Order Compact Schemes for Semilinear Poisson Equations. East Asian Journal on Applied Mathematics. 13 (1). 119-139. doi:10.4208/eajam.240222.210722
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