Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its Solution
The article considers the Van der Pol equation nonlinearity aspect related to a moving singular point. The fact of the existence of moving singular points and the uniqueness of their solution for complex domains have been proved. An answer to the question about the existence of moving singular point...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/4/873 |
| _version_ | 1797619513642975232 |
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| author | Victor Orlov |
| author_facet | Victor Orlov |
| author_sort | Victor Orlov |
| collection | DOAJ |
| description | The article considers the Van der Pol equation nonlinearity aspect related to a moving singular point. The fact of the existence of moving singular points and the uniqueness of their solution for complex domains have been proved. An answer to the question about the existence of moving singular points in the real domain was obtained. The proof of existence and uniqueness is based on an author’s modification of the technology of the classical Cauchy theorem. A priori estimates of the analytical approximate solution in the vicinity of a moving singular point are obtained. Calculations of a numerical experiment are presented. |
| first_indexed | 2024-03-11T08:28:04Z |
| format | Article |
| id | doaj.art-1e7b485ceaf1457e9f4d75f2f1e490b8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T08:28:04Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1e7b485ceaf1457e9f4d75f2f1e490b82023-11-16T21:55:12ZengMDPI AGMathematics2227-73902023-02-0111487310.3390/math11040873Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its SolutionVictor Orlov0Institute of Digital Technologies and Modeling in Construction, Moscow State University of Civil Engineering, Yaroslavskoye Shosse, 26, 129337 Moscow, RussiaThe article considers the Van der Pol equation nonlinearity aspect related to a moving singular point. The fact of the existence of moving singular points and the uniqueness of their solution for complex domains have been proved. An answer to the question about the existence of moving singular points in the real domain was obtained. The proof of existence and uniqueness is based on an author’s modification of the technology of the classical Cauchy theorem. A priori estimates of the analytical approximate solution in the vicinity of a moving singular point are obtained. Calculations of a numerical experiment are presented.https://www.mdpi.com/2227-7390/11/4/873Van der Pol equationmoving singular pointsanalytical approximate solutiona priori estimate |
| spellingShingle | Victor Orlov Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its Solution Mathematics Van der Pol equation moving singular points analytical approximate solution a priori estimate |
| title | Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its Solution |
| title_full | Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its Solution |
| title_fullStr | Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its Solution |
| title_full_unstemmed | Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its Solution |
| title_short | Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its Solution |
| title_sort | moving singular points and the van der pol equation as well as the uniqueness of its solution |
| topic | Van der Pol equation moving singular points analytical approximate solution a priori estimate |
| url | https://www.mdpi.com/2227-7390/11/4/873 |
| work_keys_str_mv | AT victororlov movingsingularpointsandthevanderpolequationaswellastheuniquenessofitssolution |