On the Validity of the Two-Timing Method for Large Times
- 1 November 1977
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 8 (6) , 1067-1091
- https://doi.org/10.1137/0508082
Abstract
In this paper we investigate the validity of the two-timing method when used to approximate the solution of an initial value problem tending to a limit cycle. It is shown that the two-timing method leads to an orbitally valid asymptotic approximation of the stable limit cycles, but that in certain situations, the two-timing method predicts an incorrect domain of attraction. As such, for certain initial values, two-timing predicts entirely incorrect long time behavior.Keywords
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