标题：Periodic averaging with a second order integral error * * This work was partly supported by CNES (the French Space Agency) under the research convention No 130777.
摘要：AbstractIn 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.
