  A Wilsonian approach based on the Similarity Renormalization Group to
$\pi\pi$ scattering is analyzed in the $JI=$00, 11 and 02 channels in momentum
space up to a maximal CM energy of $\sqrt{s}=1.4$ GeV. We identify the
Hamiltonian by means of the 3D reduction of the Bethe-Salpeter equation in the
Kadyschevsky scheme. We propose a new method to integrate the SRG equations
based in the Crank-Nicolson algorithm with a single step finite difference so
that isospectrality is preserved at any step of the calculations. We discuss
issues on the high momentum tails present in the fitted interactions hampering
calculations.
