This article is cited in 3 papers

General numerical methods

Analyticity and pseudo-analyticity in the small parameter method

V. I. Kachalov, D. A. Maslov

National Research University "Moscow Power Engineering Institute", 111250, Moscow, Russia

Abstract: The small parameter method allows one to construct solutions of differential equations in the form of power series and has become widespread in mathematical physics. In most cases, these series are asymptotically convergent. The aim of this work is to find conditions for the ordinary convergence of series in powers of a small parameter representing solutions of perturbation theory problems.

Key words: S. A. Lomov’s regularization method, holomorphic regularization, pseudo-analyticity, $\varepsilon$-regular solution, $\varepsilon$-pseudo-regular solution.

UDC: 517

Received: 27.03.2023
Revised: 27.03.2023
Accepted: 25.07.2023

DOI: 10.31857/S0044466923110170

 English version: Computational Mathematics and Mathematical Physics, 2023, 63:11, 1996–2004

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