Journal of Applied Mathematics and Stochastic Analysis
Volume 2009 (2009), Article ID 254720, 18 pages
Research Article

Implicit Difference Inequalities Corresponding to First-Order Partial Differential Functional Equations

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

Received 19 August 2008; Accepted 5 January 2009

Academic Editor: Donal O'Regan

Copyright © 2009 Z. Kamont and K. Kropielnicka. 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.


We give a theorem on implicit difference functional inequalities generated by mixed problems for nonlinear systems of first-order partial differential functional equations. We apply this result in the investigations of the stability of difference methods. Classical solutions of mixed problems are approximated in the paper by solutions of suitable implicit difference schemes. The proof of the convergence of difference method is based on comparison technique, and the result on difference functional inequalities is used. Numerical examples are presented.