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We used the SCalar Analysis of Library Enrichments (SCALEs) method to test these predictions.
An approximate solution for this model is obtained via Galérkin procedure and multiple scales method.
An approximate solution for this model is found via Galérkin procedure and the multiple scales method.
It is shown that the direct multiple scales method yields better results for the system than the ordinary discretization multiple scales method.
Then, the multiple scales method (a perturbation method) is applied to obtain the appropriate solutions.
The analysis of basic phenomena is performed using the multiple scales method.
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Almost all proseccos rely on the Charmat process, a large-scale method of producing sparkling wines, named for the French inventor, Eugène Charmat.
At last, these equations are solved by multiple-scales method.
The dynamic equations of motion of a two-element system are solved analytically using the asymptotic multiple-scales method for the weakly nonlinear system.
A separation of time-scales method is thus ideally suited to analysing this phenomenon, though we also note that more numerical techniques based upon stochastic freezing [33] could also be utilised.
The Galerkin procedure is employed to obtain the nonlinear ordinary differential equation and the multiple time-scales method is utilized to study the primary vibration resonance of the system.
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