  In this paper we present an estimate of accuracy for a piecewise polynomial
approximation of a classical numerical solution to a non linear differential
problem. We suppose the numerical solution U is computed using a grid with a
small linear step and interval time Tu, while the polynomial approximation V is
an interpolation of the values of a numerical solution on a less fine grid and
interval time Tv << Tu. The estimate shows that the interpolant solution V can
be, under suitable hypotheses, a good approximation and in general its
computational cost is much lower of the cost of the fine numerical solution. We
present two possible applications to linear case and periodic case.
