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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

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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.

Pinxia Wu, Kejia Pan, Weiwei Ling & Dongdong He. (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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