Abstract
In this paper, we introduce a variation of second order periodic averaging that is simpler to implement (than the classical high order averaging results) and allows an asymptotic reconstruction of the fast variable (φ). Providing a good estimation of φ has clear practical interest, for instance, if we use averaging in control problems where the values of φ at initial and final time are prescribed. Our approach provides an estimate of order 1, with respect to the small parameter ϵ, for both the slow and fast variables, and an estimate of order 2 for the ”moving average” of the slow variables, and not for the point-wise error. It is based on changing the initial conditions and adding first order terms to the right-hand side, but does not contain fast-oscillating near-identity transformations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
