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Aims. We wish to establish a firm link between jet simulations and analytical studies of magnetically-driven steady-state jets from Keplerian accretion disks. In particular, the latter have predicted the existence of recollimation shocks due to the dominant hoop-stress, so far never observed in platform simulations. Methods. We perform a set of axisymmetric MHD simulations of non-relativistic jets using the PLUTO code. The simulations are designed to reproduce the boundary conditions generally expected in analytical studies. We vary two parameters: the magnetic flux radial exponent $α$ and the jet mass load $κ$. In order to reach the huge unprecedented spatial scales implied by the analytical solutions, a new method allowing to boost the temporal evolution has been used. Results. We confirm the existence of standing recollimation shocks at large distances, behaving qualitatively with the mass load $κ$ as in self-similar studies. The shocks are weak and correspond to oblique shocks in a moderately high fast-magnetosonic flow. The jet emitted from the disk is focused towards the axial inner spine, which is the outflow connected to the central objet. The presence of this spine is shown to have a strong influence on jet asymptotics. Conclusions. Internal recollimation shocks may produce observable features such as standing knots of enhanced emission and a decrease of the flow rotation rate. However, more realistic simulations, e.g. fully three-dimensional, must be done in order to investigate non-axisymmetric instabilities and with ejection only from a finite zone in the disk, so as to to verify whether these MHD recollimation shocks and their properties are maintained.