A New Compact Off-Step Discretization for the System of 2D Quasi-Linear Elliptic Equations on Unequal Mesh

Abstract

We propose a new compact finite-difference discretization of O(k 2 + k 2 h 2 + h 4) using unequal mesh sizes h > 0 and k > 0 in x- and y- coordinate directions, respectively, for the solution of the system of two-dimensional quasi-linear elliptic partial differential equations subject to the appropriate Dirichlet boundary conditions. We use only three function evaluations in comparison to the five function O(k 2 + k 2 h 2 + h 4) convergence of the proposed finite difference scheme. Some numerical examples are given to illustrate the effectiveness of the proposed methods.