Studying a time‐fractional moving boundary diffusion model of solvent through a glassy polymer: A computational approach

Abstract

AbstractIn this article, a time‐fractional nonlinear moving boundary problem is considered to express the mathematical model of diffusion of a solvent into a glassy polymeric device. A numerical method, including an iterative process based on a non‐standard implicit finite difference method with variable time‐step is developed to solve this problem. The purpose of solving this problem is to study and predict the solvent diffusion behavior in the polymer and the position of the moving boundary. We analyze the monotonicity and positivity of the numerical solution. To show the effectiveness and robustness of the numerical method, two test problems are considered and the numerical results are reported for different values of model parameters.