Lie Group Analysis for Solving the Problem of Diffusion of Drugs across a Biological Membrane

Abstract

The Lie group method is applied to study the diffusion process of drugs across a biological membrane which tends to partially absorb the drug. For the diffusion coefficient, we considered two cases. The Lie group analysis is based on reducing the number of independent variables by one, and consequently the mathematical model described by nonlinear partial differential equation to, covers the diffusion process with the boundary and initial conditions, and is transformed into an ordinary differential equation with the corresponding conditions. The obtained nonlinear ordinary differential equation is solved numerically using the ${4^{th}}$ and ${5^{th}}$ Runge Kutta method, and the results are illustrated graphically and in tables too.