Fourth order finite difference methods for the system of 2-d nonlinear elliptic equations with variable coefficients

Abstract

This paper attempts to trace out the fourth order finite difference methods for solving the system of two dimensional nonlinear elliptic equations with variable coefficients using 9-grid points subject to Dirichlet boundary conditions. The methods have been tested on various important problems including 2-D viscous, incompressible Navier-Stokes equations. The numerical results show that the proposed methods produce oscillation free solutions for high Reynolds number.