“In the Method of Multiple Time Scales, the single time variable is replaced by an infinite sequence of independent time scales. The price paid for this freedom is that the well-known solvability conditions, which guarantee the elimination of secular terms in the fast variable, T0 = t, impose consistency constraints on the structure of the approximate solution. Specifically, mutual consistency of solvability conditions that pertain to different orders must be ensured. This requirement limits the freedom of choice of amplitudes of “free” resonant terms, which appear in each order of the expansion. If the constraints are not obeyed, then the analysis may lead to wrong results, or allow only trivial solutions. It is pointed out that, different choices of the free amplitudes, lead to conflicting results.” - Peter Kahn and Yair Zarmi (2017).

Considering the LIMITATIONS OF METHOD OF MULTIPLE SCALES, what's the maximum error in the use of the method for the solution of a nonlinear problem ?