A Finite Difference Procedure for Solving Coupled, Nonlinear Elliptic Partial Differential Equations
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.
Published in Computers & Chemical Engineering, Volume 11, Issue 5, 1987, pages 543-546.
Copyright 1987, Elsevier.
Nguyen, T. V. & White, R. E. (1987). A Finite Difference Procedure for Solving Coupled, Nonlinear Elliptic Partial Differential Equations. Computers & Chemical Engineering, 11 (5), 543 – 546. http://dx.doi.org/10.1016/0098-1354(87)80029-7