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Volume 15
Issue 6
10.3390/sym15061200
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Article

The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain

by
Victor Orlov
1,* and
Alexander Chichurin
2
1
Institute of Digital Technologies and Modeling in Construction, Moscow State University of Civil Engineering, Yaroslavskoe Shosse, 26, Moscow 129337, Russia
2
Department of Mathematical Modeling, The John Paul II Catholic University of Lublin, ul. Konstantynów 1H, 20-708 Lublin, Poland
*
Author to whom correspondence should be addressed.
Symmetry 2023, 15(6), 1200; https://doi.org/10.3390/sym15061200
Submission received: 12 March 2023 / Revised: 30 March 2023 / Accepted: 31 May 2023 / Published: 3 June 2023
(This article belongs to the Special Issue Symmetries of Difference Equations, Special Functions and Orthogonal Polynomials II)
Versions Notes

Abstract

In this paper, we substantiate the analytical approximate method for Cauchy problem of the Van der Pol equation in the complex domain. These approximate solutions allow analytical continuation for both real and complex cases. We follow the influence of variation in the initial data of the problem in order to control the computational process and improve the accuracy of the final results. Several simple applications of the method are given. A numerical study confirms the consistency of the developed method.
Keywords: nonlinear differential equation of the second order; movable singular point; analytical approximate solution nonlinear differential equation of the second order; movable singular point; analytical approximate solution

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MDPI and ACS Style

Orlov, V.; Chichurin, A. The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain. Symmetry 2023, 15, 1200. https://doi.org/10.3390/sym15061200

AMA Style

Orlov V, Chichurin A. The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain. Symmetry. 2023; 15(6):1200. https://doi.org/10.3390/sym15061200

Chicago/Turabian Style

Orlov, Victor, and Alexander Chichurin. 2023. "The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain" Symmetry 15, no. 6: 1200. https://doi.org/10.3390/sym15061200

APA Style

Orlov, V., & Chichurin, A. (2023). The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain. Symmetry, 15(6), 1200. https://doi.org/10.3390/sym15061200

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