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A Method of the Study of the Cauchy Problem for a Singularly Perturbed Linear Inhomogeneous Differential Equation

Classical Analysis and ODEs 2017-11-23 v1

Abstract

We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the deviation (in the norm of the space of continuous functions) of its nnth element from the solution of the problem is proportional to the (n+1)(n+1)th power of the parameter of perturbation. This sequence can be used for justification of asymptotics obtained by the method of boundary functions.

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Cite

@article{arxiv.1711.08050,
  title  = {A Method of the Study of the Cauchy Problem for a Singularly Perturbed Linear Inhomogeneous Differential Equation},
  author = {Evgeny E. Bukzhalev and Alexey V. Ovchinnikov},
  journal= {arXiv preprint arXiv:1711.08050},
  year   = {2017}
}

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12 pages