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