Transient behavior of the solutions to the second order difference equations by the renormalization method based on Newton-Maclaurin expansion
Mathematical Physics
2017-09-08 v1 Analysis of PDEs
Classical Analysis and ODEs
Dynamical Systems
math.MP
Computational Physics
Abstract
The renormalization method based on the Newton-Maclaurin expansion is applied to study the transient behavior of the solutions to the difference equations as they tend to the steady-states. The key and also natural step is to make the renormalization equations to be continuous such that the elementary functions can be used to describe the transient behavior of the solutions to difference equations. As the concrete examples, we deal with the important second order nonlinear difference equations with a small parameter. The result shows that the method is more natural than the multi-scale method.
Keywords
Cite
@article{arxiv.1709.02044,
title = {Transient behavior of the solutions to the second order difference equations by the renormalization method based on Newton-Maclaurin expansion},
author = {Cheng-shi Liu},
journal= {arXiv preprint arXiv:1709.02044},
year = {2017}
}
Comments
12 pages