@Article{NMTMA-16-2,
author = {Hu, Hongling and Pan, Kejia and Zhilin, Li and Kang, Fu and Li, Jin and Hu, Hongling and Zhilin, Li},
title = {New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2023},
volume = {16},
number = {2},
pages = {393--409},
abstract = {<p style="text-align: justify;">Some new sixth-order compact finite difference schemes for Poisson/Helmholtz equations on rectangular domains in both two- and three-dimensions are
developed and analyzed. Different from a few sixth-order compact finite difference
schemes in the literature, the finite difference and weight coefficients of the new
methods have analytic simple expressions. One of the new ideas is to use a weighted
combination of the source term at staggered grid points which is important for grid
points near the boundary and avoids partial derivatives of the source term. Furthermore, the new compact schemes are exact for 2D and 3D Poisson equations if the
solution is a polynomial less than or equal to 6. The coefficient matrices of the new
schemes are $M$-matrices for Helmholtz equations with wave number $K≤0,$ which
guarantee the discrete maximum principle and lead to the convergence of the new
sixth-order compact schemes. Numerical examples in both 2D and 3D are presented
to verify the effectiveness of the proposed schemes.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2022-0073},
url = {https://global-sci.com/article/90212/new-sixth-order-compact-schemes-for-poissonhelmholtz-equations}
}