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Symbolic derivation of finite difference approximations for the three‐dimensional Poisson equation
Author(s) -
Gupta Murli M.,
Kouatchou Jules
Publication year - 1998
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199809)14:5<593::aid-num4>3.0.co;2-d
Subject(s) - mathematics , partial differential equation , finite difference , finite difference coefficient , finite difference method , poisson distribution , differential equation , point (geometry) , partial derivative , simple (philosophy) , scheme (mathematics) , poisson's equation , mathematical analysis , order (exchange) , finite element method , mixed finite element method , geometry , philosophy , statistics , physics , epistemology , thermodynamics , finance , economics
A symbolic procedure for deriving various finite difference approximations for the three‐dimensional Poisson equation is described. Based on the software package Mathematica, we utilize for the formulation local solutions of the differential equation and obtain the standard second‐order scheme (7‐point), three fourth‐order finite difference schemes (15‐point, 19‐point, 21‐point), and one sixth‐order scheme (27‐point). The symbolic method is simple and can be used to obtain the finite difference approximations for other partial differential equations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 593–606, 1998