Fourth‐order difference methods for the system of 2D nonlinear elliptic partial differential equations

Abstract

Abstract 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.