Statistics for 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.