Holomorphic Regularization of Singularly Perturbed Integro-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 Moscow Pleiades Publishing 01.01.2024
Springer
Subjects
Difference and Functional Equations
Differential equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
essentially singular manifold
integro-differential equation
S.A. Lomov’s regularization method
pseudoholomorphic solution
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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.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266124010014