Holomorphic Regularization of Singularly PerturbedIntegro-Differential Equations

S.A. Lomov’s regularization method has long been used to solve integro-differential singularly perturbed equations, which are very important from the viewpoint of applications. In this method, the series in powers of a small parameter representing the solutions of these equations converge asymptotic...

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Bibliographic Details
Published inDifferential equations Vol. 60; no. 1; pp. 1 - 11
Main Authors Besov, V S, Kachalov, V I
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.01.2024
Subjects
Analytic functions
Convergence
Differential equations
Mathematical analysis
Perturbation theory
Regularization
Singular perturbation
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Summary:S.A. Lomov’s regularization method has long been used to solve integro-differential singularly perturbed equations, which are very important from the viewpoint of applications. In this method, the series in powers of a small parameter representing the solutions of these equations converge asymptotically. However, in accordance with the main concept of the method, to construct a general singular perturbation theory one must indicate conditions for the ordinary convergence of these series. This is the subject of the present paper.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266124010014