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Fourth‐order difference methods for the system of 2D nonlinear elliptic partial differential equations
Author(s) -
Jain M. K.,
Jain R. K.,
Mohanty R. K.
Publication year - 1991
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.1690070303
Subject(s) - mathematics , nonlinear system , mathematical analysis , partial differential equation , elliptic partial differential equation , finite difference method , dirichlet problem , compressibility , dirichlet boundary condition , boundary value problem , mechanics , physics , quantum mechanics
We present the fourth‐order finite difference methods for the system of 2D nonlinear elliptic equations using 9‐grid points on a square region R subject to Dirichlet boundary conditions. The method has been tested on viscous, incompressible 2D Navier‐Stokes equations. The numerical results show that the proposed methods produce accurate and oscillation‐free solutions for large Reynolds numbers.