A second order method for a drug release process defined by a differential Maxwell-Wichert stress-strain relation

Abstract

Polymeric drug delivery platforms offer promising capabilities for controlled drug release thanks to their ability to be custom-designed with specific properties. In this paper we present a model to simulate the complex interplay between solvent absorption, polymer swelling, drug release and stress development within these platforms. A system of nonlinear partial differential equations coupled with an ordinary differential equation is introduced to avoid drawbacks from other models found in the literature. These incorporated a memory effect but from a numerical standpoint, required storing all previous time steps, making them computationally expensive. This paper proposes a new numerical method to simulate such devices based on nonuniform grids and an implicit midpoint time discretization. Our main results are the second order convergence of the method for nonsmooth solutions and the scheme’s stability under the assumption of quasiuniform grids and a small enough timestep