Statistics – Applications
Scientific paper
Aug 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976jimia..18...87v&link_type=abstract
Institute of Mathematics and Its Applications, Journal, vol. 18, Aug. 1976, p. 87-98.
Statistics
Applications
Asymptotic Methods, Boundary Layer Equations, Mass Transfer, Two Body Problem, Celestial Mechanics, Iterative Solution, Nonlinear Equations, Numerical Stability, Perturbation Theory
Scientific paper
In studying models for the two-body problem with quick loss of mass a boundary layer problem arises for a third-order system of nonlinear ordinary differential equations. The models are identified by a real parameter n with n not less than 1. It turns out that for n equal to 1 asymptotic approximations of the solutions can be obtained by applying the method of matched asymptotic expansions according to Vasil'eva or a multiple time scales method developed by O'Malley. For n greater than 1 these methods break down and it is shown that this is due to the occurrence of 'unexpected' order functions in the asymptotic expansions. The expansions for n greater than 1 are obtained by constructing an inner and outer expansion of the solution and matching these by the process of taking intermediate limits.
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