Drug release from viscoelastic polymeric matrices : a stable and supraconvergent FDM

Abstract Drug release from viscoelastic polymeric matrices is a complex phenomenon where the main actors are the fluid, the polymeric structure and the drug. As the fluid enters into the polymer, the polymeric chains relax inducing a resistance to the fluid entrance. In contact with the fluid, a dissolution processes takes place and the dissolved drug diffuses through the medium. Our main goal in this paper is to propose a stable finite difference method that leads to supraconvergent approximations for the fluid, solid and dissolved drug concentrations. The analysis proposed is non-standard in the sense that the error estimates have an important role in the stability analysis.