Holomorphic Regularization of Singularly Perturbed Integro-Differential Equations

Pub Date : 2024-04-09 DOI:10.1134/s0012266124010014

V. S. Besov, V. I. Kachalov

引用次数: 0

Abstract

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.

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奇异扰动积分微分方程的全态正则化

摘要 S.A.洛莫夫正则化方法长期以来一直被用于求解从应用角度来看非常重要的微分正则方程。在这种方法中，代表这些方程解的小参数幂级数会逐渐收敛。然而，根据该方法的主要概念，要构建一般奇异扰动理论，必须指出这些序列普通收敛的条件。这就是本文的主题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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