Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the method of strained parameters and the method of averaging

Author: D. P. Mason
Journal: Quart. Appl. Math. 42 (1984), 77-85
MSC: Primary 34C29
DOI: https://doi.org/10.1090/qam/736507
MathSciNet review: 736507
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Abstract: The method of multiple scales can be modified to remove remaining undesirable features in the perturbation solution by expanding available parameters in the equation(s) (Veronis [1]). Corresponding modifications to the Lindstedt-Poincaré method of strained parameters and the method of averaging are investigated and illustrated using the Duffing equation. It is found that a solution to the Duffing equation with no secular terms in either the amplitude or the frequency can be obtained simply by expanding the parameter in the equation without making the near-identity transformation of the independent variable associated with the Lindstedt-Poincaré technique.

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DOI: https://doi.org/10.1090/qam/736507
Article copyright: © Copyright 1984 American Mathematical Society

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