The parabolic problem: (1) \(u_ t-\nabla \cdot (D(\chi,t)\nabla u)=f(\chi,t,u)\) for \(x\in \Omega\), \(0\leq t\leq T\); \(\alpha (\chi_ 0)\partial u/\partial \nu +\beta (\chi_ 0)u=h(\chi_ 0,t)\) for \(\chi_ 0\in \partial \Omega\), \(0\leq t\leq T\), and \(u(0,\chi)=\psi (\chi)\) for \(\chi\in \Omega\) is approximated in the usual way by an implicit difference scheme. The purpose of the paper is to present iterative methods to solve directly the finite difference problem and to prove the convergence of its solution to that of (1). Two schemes based on the Jacobi and Gauss-Seidel methods for nonlinear algebraic equations are proposed, which eliminate the drawback of the usual iterative processes, consisting in the necessity in solving al each step of a linear system. The basic idea of the paper is to extend to the discrete case the monotonic approach to the exact solution. An interesting property of both schemes is that they preserve monotonicity, thus enabling the authors to derive error estimates as well as stability criteria.