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 th element from the solution of the problem is proportional to the th power of the parameter of perturbation. This sequence can be used for justification of asymptotics obtained by the method of boundary functions.
Keywords
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