  We determine sizes and activation energies of k{\pi}-skyrmions on a discrete
lattice using the Landau- Lifshitz-Gilbert equation and the geodesic nudged
elastic band method. The employed atomic material parameters are based on the
skyrmionic material system Pd/Fe/Ir(111). We find that the critical magnetic
fields for collapse of the 2{\pi}-skyrmion and 3{\pi}-skyrmion are very close
to each other and considerably lower than the critical field of the
1{\pi}-skyrmion. The activation energy protecting the structures does not
strictly decrease with increasing k as it can be larger for the 3{\pi}-skyrmion
than for the 2{\pi}-skyrmion depending on the applied magnetic field.
Furthermore, we propose a method of switching the skyrmion order k by a
reversion of the magnetic field direction in samples of finite size.
