Multiple-scale analysis of dynamical systems on the lattice

  title={Multiple-scale analysis of dynamical systems on the lattice},
  author={Decio Levi and Piergiulio Tempesta},
  journal={Journal of Mathematical Analysis and Applications},
  • D. Levi, P. Tempesta
  • Published 2011
  • Mathematics
  • Journal of Mathematical Analysis and Applications
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… Expand
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