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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 517285, 10 pages
http://dx.doi.org/10.1155/2014/517285
Research Article

The Method of Lines for Ternary Diffusion Problems

Institute of Mathematics, University of Gdańsk, Wit Stwosz Street 57, 80-952 Gdańsk, Poland

Received 9 December 2013; Revised 26 February 2014; Accepted 3 March 2014; Published 28 April 2014

Academic Editor: Alvaro H. Salas

Copyright © 2014 Henryk Leszczyński and Milena Matusik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 norms is investigated. Numerical examples confirm the parabolic behaviour of this model and very regular dynamics.