The study of transport equations, particularly, the differentials parabolic partial   equation of lineal nature, is perhaps a highly important aspects in the field of the   mathematical physics. A comparison of the analytical results with numerical by   means of a the use of powerful methods of numerical solutions appears to a classic   problem, as is it the conduction of the heat in materials. If simulations were carried   out by means of the elaborations of a program written in the languages Fortran 90   and C++. The analytical solutions to the created problem is obtained by means of the   use of Laplace transformed instead of the traditional method of separation of   variables.