Title: Transient behavior of the solutions to the second order difference equations by the renormalization method based on Newton-Maclaurin expansion,
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.