English

Lagrange's discrete model of the wave equation in dimension greater than one

Dynamical Systems 2023-07-14 v1

Abstract

A celebrated theorem of Lagrange states that a solution of the wave equation with one-dimensional space variable is the uniform limit, as N tends to infinity, of a second order ODE obtained from a mechanical model discretizing a string as N identical harmonic oscillators. Answering to a question posed by G. Gallavotti we generalize this result to the case of any space dimension.

Keywords

Cite

@article{arxiv.2307.06347,
  title  = {Lagrange's discrete model of the wave equation in dimension greater than one},
  author = {Massimo Villarini},
  journal= {arXiv preprint arXiv:2307.06347},
  year   = {2023}
}