Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A note on the method of multiple scales


Author: George Veronis
Journal: Quart. Appl. Math. 38 (1980), 363-368
MSC: Primary 34A25
DOI: https://doi.org/10.1090/qam/592203
MathSciNet review: 592203
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Abstract: A modification of the method of multiple scales makes use of the expansion of parameters of the system in order to remove undesirable characteristics of the solution obtained by the usual multiple-scale method. When applied to the damped harmonic oscillator, the modification leads to the exact solution. For the Duffing equation it leads to an approximation which can be reduced to the solution reported by Nayfeh [1], However, the solution derived here appears to be more accurate and the frequency takes on a form without nonuniformities.


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DOI: https://doi.org/10.1090/qam/592203
Article copyright: © Copyright 1980 American Mathematical Society


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