Asymptotic Solutions And Error Estimates For Linear Systems Of Difference And Differential Equations
Journal Of Mathematical Analysis And Applications
Mathematics and Computer Science
Classical results concerning the asymptotic behavior solutions of systems of linear differential or difference equations lead to formulas containing factors that are asymptotically constant, i.e., k+o(1) as t tends to infinity. Here we are interested in more precise information about the o(1) terms, specifically how they depend precisely on certain perturbation terms in the equation. Results along these lines were given by Gel'fond and Kubenskaya for scalar difference equations and we will both extend and generalize one of them as well as provide some corresponding results for differential equations.
Bodine, Sigrun, and D. A. Lutz. 2004. "Asymptotic solutions and error estimates for linear systems of difference and differential equations." Journal Of Mathematical Analysis And Applications 290(1): 343-362.