International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 48, Pages 3059-3066

Accurate solution estimates for vector difference equations

Rigoberto Medina

Departamento de Ciencias Exactas, Universidad de Los Lagos, Casilla 933, Osorno, Chile

Received 10 October 2002

Copyright © 2003 Rigoberto Medina. 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.


Accurate estimates for the norms of the solutions of a vector difference equation are derived. They give us stability conditions and bounds for the region of attraction of the stationary solution. Our approach is based on estimates for the powers of a constant matrix. We also discuss applications of our main results to partial reaction-diffusion difference equations and to a Volterra difference equation.