A NEW HIGH ACCURACY VARIABLE MESH DISCRETIZATION FOR THE SOLUTION OF THE SYSTEM OF 2D NON-LINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS

摘要

In this paper, we develop an O(k~2+ k~2h_1+h_1~3 ) nine-point compact off-step finite difference　discretization for the solution of the system of two-dimensional non-linear elliptic equations subject to Dirichlet boundary conditions, by using variable mesh lengths h_1 in x-direction and a constant mesh length k in j-direction. We use only three function evaluations. Further we discuss the conditions for the convergence of the iterative methods applied to the system of difference equations so framed for the steady state 2D convection-diffusion equation. Numerical illustrations of some benchmark problems including 2D non-linear convection equation and 2D steady-state Navier-stokes equations of motion are provided to depict the efficiency of the method.