International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 48, Pages 3059-3066
doi:10.1155/S016117120321022X

Accurate solution estimates for vector difference equations

Abstract

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.