Error bounds for perturbation methods

Details Error bounds for perturbation methods Error bounds for perturbation methods

Nov 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976cemec..14..351k&link_type=abstract

(Conference on Mathematical Methods in Celestial Mechanics, 5th, Oberwolfach, West Germany, Aug. 24-30, 1975.) Celestial Mechani

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Boundary Value Problems, Celestial Mechanics, Error Analysis, Perturbation Theory, Differential Equations, Lipschitz Condition, Periodic Variations, Systems Stability, Taylor Series

Scientific paper

There are many papers dealing with the problem of error bounds for perturbation methods (development with respect to a small parameter, method of averaging, and others). The majority of these bounds, however, is very pessimistic and does not really reflect the qualities of the underlying perturbation method. In this paper, an attempt is made to overcome this problem. By using a comparison theorem and the high-order approximations, both upper bounds and lower bounds are established.

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