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Algorithm of the Regularization Method for a Nonlinear Singularly Perturbed Integro-Differential Equation with Rapidly Oscillating Inhomogeneities

  • INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS
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Abstract

Lomov’s regularization method is generalized to nonlinear singularly perturbed integro-differential equations with rapidly oscillating right-hand side. The influence of the kernel of the integral operator, the nonlinearity, and the rapidly oscillating part on the asymptotics of the solution of the initial value problem for these equations is established. Previously, singularly perturbed linear systems of this type and nonlinear systems without oscillating inhomogeneity were studied.

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Notes

  1. Here and in the following, the superscript \(m \) in parentheses in \(y^{(m)} \) means \(y^{(m_1,m_2)} \) and is the number of the coefficient \(y^{(m)} \). It should not be confused with the number of derivative.

  2. Here and in what follows, a bold dot as a superscript on a parenthesis means differentiation with respect to \(t \) of the expression in the parentheses.

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Authors and Affiliations

  1. National Research University “Moscow Power Engineering Institute”, Moscow, 111250, Russia

    A. A. Bobodzhanov & V. F. Safonov

  2. Akhmet Yassawi International Kazakh–Turkish University, Turkestan, Kazakhstan

    B. T. Kalimbetov

Authors
  1. A. A. Bobodzhanov
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  2. B. T. Kalimbetov
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  3. V. F. Safonov
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Correspondence to A. A. Bobodzhanov, B. T. Kalimbetov or V. F. Safonov.

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Translated by V. Potapchouck

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Bobodzhanov, A.A., Kalimbetov, B.T. & Safonov, V.F. Algorithm of the Regularization Method for a Nonlinear Singularly Perturbed Integro-Differential Equation with Rapidly Oscillating Inhomogeneities. Diff Equat 58, 392–404 (2022). https://doi.org/10.1134/S0012266122030090

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