Existence of a waiting time in a discrete two-phase Stefan problem

In this paper we consider a one-dimensional heat conduction problem, with initial datum and with mixed boundary conditions. We obtain, with an implicit finite difference scheme, some sufficient conditions, so that the discrete solution is positive at any moment if it is positive at the previous time step. We deduce, with an explicit finite difference scheme, the discrete expression of the temperature at each time step, as a polynomial in the variable lambda = alpha((Delta t)/(Delta x(2))), with coefficients given as function of the problem dates. So we can establish some sufficient conditions on the data in order to obtain the existence of a waiting time at which a phase-change begins. (C) 2000 Elsevier Science Inc. All rights reserved.