A fourth?order finite difference scheme for two?dimensional nonlinear elliptic partial differential equations

Abstract

A finite difference scheme for the two?dimensional, second?order, nonlinear elliptic equation is developed. The difference scheme is derived using the local solution of the differential equation. A 13?point stencil on a uniform mesh of size h is used to derive the finite difference scheme, which has a truncation error of order h4. Well?known iterative methods can be employed to solve the resulting system of equations. Numerical results are presented to demonstrate the fourth?order convergence of the scheme. 1995 John Wiley & Sons, Inc. Copyright 1995 Wiley Periodicals, Inc.