Abstract
There are many papers dealing with the problem of error bounds for perturbation methods (development with respect to a small parameter, method of averaging, stroposcopic method etc.). The majority of these bounds, however, is very pessimistic and does not really reflect the qualities of the underlying perturbation method. In this paper a new attempt is made to overcome this problem. By using a new comparison theorem and the higher order approximations we are led not only to upper bounds, but to lower bounds as well.
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Kirchaber, U. Error bounds for perturbation methods. Celestial Mechanics 14, 351–362 (1976). https://doi.org/10.1007/BF01228521
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DOI: https://doi.org/10.1007/BF01228521