In this talk we are interested in approximating the solution of one
dimensional parabolic singularly perturbed problems of reaction-diffusion type. 
We construct a numerical method combining the Crank-Nicolson method on a 
uniform mesh, to discretize in time, and the classical central finite difference 
scheme, on a special nonuniform mesh condensing the grid points in the 
boundary layer regions, to discretize in space. We prove that the fully discrete 
scheme is a second order parameter uniform convergent method in the 
maximum norm. The proof of the convergence is based on splitting the 
contribution to the global error of both the time and the spatial discretizations. 
We show the results obtained for different test problems, illustrating in practice 
the order of uniform convergence of the numerical method.