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HIGH‐ORDER‐ACCURATE DISCRETIZATION STENCIL FOR AN ELLIPTIC EQUATION
Author(s) -
ARAD M.,
YAKHOT A.,
BENDOR G.
Publication year - 1996
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19960830)23:4<367::aid-fld426>3.0.co;2-g
Subject(s) - stencil , discretization , mathematics , laplace operator , dirichlet distribution , elliptic operator , mathematical analysis , boundary value problem , operator (biology) , order (exchange) , boundary (topology) , neumann boundary condition , elliptic curve , scheme (mathematics) , dirichlet problem , computational science , biochemistry , chemistry , finance , repressor , transcription factor , economics , gene
The coefficients for a nine‐point high‐order‐accurate discretization scheme for an elliptic equation ∇ 2 u − γ 2 u = r 0 (∇ 2 is the two‐dimensional Laplacian operator) are derived. Examples with Dirichlet and Neumann boundary condtions are considered. In order to demonstrate the high‐order accuracy of the method, numerical results are compared with exact solutions.