The Method of Lines for Ternary Diffusion Problems

Abstract

The method of lines (MOL) for diffusion equations with Neumann boundary conditions is considered. These equations are transformed by a discretization in space variables into systems of ordinary differential equations. The proposed ODEs satisfy the mass conservation law. The stability of solutions of these ODEs with respect to discrete L² norms and discrete $W^{1,\infty }$ norms is investigated. Numerical examples confirm the parabolic behaviour of this model and very regular dynamics.