An Efficient EXCMG-Newton Method Combined with Fourth-Order Compact Schemes for Semilinear Poisson Equations

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.

Author Details

Pinxia Wu

Kejia Pan

Weiwei Ling

Dongdong He

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