  In this work we present a method, based on the use of Bernstein polynomials,
for the numerical resolution of some boundary values problems. The computations
have not need of particular approximations of derivatives, such as finite
differences, or particular techniques, such as finite elements. Also, the
method doesn't require the use of matrices, as in resolution of linear
algebraic systems, nor the use of like-Newton algorithms, as in resolution of
non linear sets of equations. An initial equation is resolved only once, then
the method is based on iterated evaluations of appropriate polynomials.
