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Technical note: The numerical solution of the system of 3‐D nonlinear elliptic equations with mixed derivatives and variable coefficients using fourth‐order difference methods
Author(s) -
Mohanty R. K.,
Jain M. K.
Publication year - 1995
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/num.1690110303
Subject(s) - mathematics , mathematical analysis , nonlinear system , singularity , dirichlet problem , elliptic curve , dirichlet boundary condition , variable (mathematics) , boundary value problem , physics , quantum mechanics
In this article, we report two fourth‐order difference methods for the numerical integration of the system of general 3‐D nonlinear elliptic equations subject to Dirichlet boundary conditions on a uniform cubic grid. When the coefficients of u xy , u yz , and u zx are not equal to zero and the coefficients of u xx , u yy , and u zz are equal, we require 27 grid points; when the coefficients of u xy , u yz , and u zx are equal to zero, we require only 19 grid points. The utility of the new methods is shown by testing the methods on various examples, including 3‐D steady state viscous incompressible Navier–Stokes' model equations and Poisson's equation in polar coordinates, which confirm the accurate and oscillation‐free solutions for large Reynolds numbers even in the vicinity of singularity. © 1995 John Wiley & Sons, Inc.