A finite difference procedure for solving coupled, nonlinear elliptic partial differential equations

Abstract

A finite difference procedure is presented for solving coupled sets of partial differential equations. For one dependent variable, the procedure consists of replacing the concept of a single unknown at multiple grid points with the concept of a line of node points with multiple unknowns at each node point. The procedure is illustrated first for a second order, linear elliptic partial differential equation and then for a coupled set of non-linear elliptic partial differential equations. The method is easier to use and requires less computer storage than a banded solver method such as IMSL's routine LEQT1B. The procedure could be extended to include three spatial coordinates and time.