A non-overlapping domain decomposition technique applied to the finite difference method is presented for the numerical solution of the forward-backward heat equation in the case of one-dimension. While the previous attempts to deal with this problem have been based on an iterative domain decomposition scheme, the current work avoid iterations. Also a physical matching condition is suggested to avoid difficulties caused by the interface boundary nodes and obtain a square system of equations. In addition, the convergence and stability of the proposed method is investigated. Some numerical experiments are given to show the effectiveness of the proposed method.
