Summary: A “scheme of fractional steps type”, associated to the nonlinear phase-field transition system with non-homogeneous Cauchy-Neumann boundary conditions, is considered in the present paper. To approximate the solution of the linear parabolic system introduced by such approximating scheme, a cubic spline method have been used. A stability result for this new approach is proved and some numerical experiments, like simulation of “separation zone” between the phases of the material that is involved in the solidification process, are performed too.