Seminarium Nieliniowość i Geometria

We review the ideas of conditional symmetries as introduced by Bluman and Cole in 1969 and of symmetry preserving discretizations. We apply these ideas constructing some discrete models of the Boussinesq equation on different lattices preserving some of its conditional symmetries.We carry out the symmetry reduction of the obtained nonlinear discrete schemes with respect to the conditional symmetries and obtain the reduced discrete equations. A numerical comparison with the exact continuous solution given by Weierstrass elliptic functions is carried out.