On the holomorphic regularization of singularly perturbed systems of differential equations
type: Item
instance of: scholarly article
title: On the holomorphic regularization of singularly perturbed systems of differential equations
zbMATH Open document ID: 1384.34068
DOI: 10.1134/S0965542517040054
author: V. I. Kachalov
published in: Computational Mathematics and Mathematical Physics
publication date: 2017-12-06T00:00:00Z
review text: The paper deals with a holomorphic regularization based on Lomov's regularization method for the singularly perturbed system \[ \varepsilon y'=f(t,y),\;t\in[0,T],\;y\in\mathbb{R}^k, \;y(0,\varepsilon)=y_0. \] The original nonlinear problem is reduced to a linear problem studied as a regular one by using the asymptotic expansion techniques, and subsequently, the implicit function theorem is applied to show that the solution of the Cauchy problem under consideration is pseudo-holomorphic in the global sense.
reviewed by: Robert Vrabel
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 6815869
zbMATH Keywords: Lomov's regularization method
zbMATH Keywords: holomorphic regularization
zbMATH Keywords: pseudo-holomorphic solution
zbMATH Keywords: integrals holomorphic in a small parameter
zbMATH Keywords: singularly perturbed systems of differential equations
zbMATH Keywords: sufficient conditions for convergence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6815869