High-order implicit finite difference schemes for the two-dimensional Poisson equation
Por:
Zapata, Miguel Uh, Balam, Reymundo Itza
Publicada:
15 sep 2017
Resumen:
In this paper, a new family of high-order finite difference schemes is
proposed to solve the two-dimensional Poisson equation by implicit
finite difference formulas of (2M + 1) operator points. The implicit
formulation is obtained from Taylor series expansion and wave plane
theory analysis, and it is constructed from a few modifications to the
standard finite difference schemes. The approximations achieve
(2M+4)-order accuracy for the inner grid points and up to eighth-order
accuracy for the boundary grid points. Using a Successive
Over-Relaxation method, the high-order implicit schemes have faster
convergence as M is increased, compensating the additional computation
of more operator points. Thus, the proposed solver results in an
attractive method, easy to implement, with higher order accuracy but
nearly the same computation cost as those of explicit or compact
formulation. In addition, particular case M = 1 yields a new compact
finite difference schemes of sixth-order of accuracy. Numerical
experiments are presented to verify the feasibility of the proposed
method and the high accuracy of these difference schemes. (C) 2017
Elsevier Inc. All rights reserved.
Filiaciones:
Zapata, Miguel Uh:
CONACYT Ctr Invest Matemat AC, CIMAT Unidad Merida, Merida, Yucatan, Mexico
Balam, Reymundo Itza:
Univ Autonoma Mexico UNAM, Fac Ciencias, Ciudad Univ, Mexico City, DF, Mexico
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