The rotation profile of a magnetized plasma cylinder composed of multiple fluids is investigated analytically, expanding on previous results. The analytic steady-state solution is used as a benchmark for a time-dependent multiple-fluid finite-difference code, MITNS: Multiple-Ion Transport Numerical Solver. Magnetic field evolution is taken into account, both analytically and numerically. Its details are shown to be of importance when particles are allowed out of the domain. MITNS reproduces the asymptotic expansion results for a small parameter $\deltaěrymuchless$1. For me/mi$\simδ\ll$1, a slightly different regime, dominated by viscosity-induced transport of ions, is found numerically and analytically. This verification supports the use of this code for more complex time-dependent calculations in the future. Additionally, we derive the angular velocity profile of each species due to radial particle and charge fluxes of various strengths.