Geodesic
On the two-scale method for the problem of perturbed one-frequency oscillations
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 383-389

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We consider the asymptotic behavior with respect to time of the solution to the initial problem for an ordinary differential equation with a small parameter $\varepsilon$. We construct an asymptotic approximation that is valid for time values $t\gg\varepsilon$ up to any order in $\varepsilon$. 
@article{TMF_1999_118_3_a7,
     author = {A. M. Il'in},
     title = {On the two-scale method for the problem of perturbed one-frequency oscillations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {383--389},
     publisher = {mathdoc},
     volume = {118},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a7/}
}
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A. M. Il'in. On the two-scale method for the problem of perturbed one-frequency oscillations. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 383-389. http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a7/