We propose a new approach to the multiple-scale analysis of difference equations, in the context of the finite operator calculus. We derive the transformation formulae that map any given dynamical system, continuous or discrete, into a rescaled discrete system, by generalizing a classical result due to Jordan. Under suitable analytical hypotheses on the function space we consider, the rescaled equations are of finite order. Our results are applied to the study of multiple-scale reductions of dynamical systems, and in particular to the case of a discrete nonlinear harmonic oscillator. (C) 2010 Elsevier Inc. All rights reserved.
Levi, D., Tempesta, P. (2011). Multiple-scale analysis of dynamical systems on the lattice. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 376(1), 247-258 [10.1016/j.jmaa.2010.09.053].
Multiple-scale analysis of dynamical systems on the lattice
LEVI, Decio;
2011-01-01
Abstract
We propose a new approach to the multiple-scale analysis of difference equations, in the context of the finite operator calculus. We derive the transformation formulae that map any given dynamical system, continuous or discrete, into a rescaled discrete system, by generalizing a classical result due to Jordan. Under suitable analytical hypotheses on the function space we consider, the rescaled equations are of finite order. Our results are applied to the study of multiple-scale reductions of dynamical systems, and in particular to the case of a discrete nonlinear harmonic oscillator. (C) 2010 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
