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arXiv · 1711.08050

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

Evgeny E. Bukzhalev·Alexey V. Ovchinnikov
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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 $n$th element from the solution of the problem is proportional to the $(n+1)$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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Evgeny E. Bukzhalev, Alexey V. Ovchinnikov. 2017-11-08. A Method of the Study of the Cauchy Problem for a Singularly Perturbed Linear Inhomogeneous Differential Equation. https://arxiv.org/abs/1711.08050

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