In this work an algebraic-differential mathematical model for the simulation of the drug release dynamics from a drug-eluting stent is presented. The mathematical model is based on a diffusion-reaction system for the drug's concentrations in the liquid and solid phases.The erosion effect is accounted for by the Pseudo-Steady-State-Approximation (PSSA), leading to a time depending model for the moving spatial surface's coordinate. In the model the effects of the two diffusions, in solid and liquid phase respectively, is accounted. Due to the different time scales of the diffusion and reaction, the mathematical model is close to be stiff. This leads us to adopt an Implicit-Explicit (ImEx) time discretization, treating the diffusion term implicitly and the reaction term explicitly. The space derivatives are discretized using Finite-Element method choosing opportunely the functional space.