The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/6/1200 |
| _version_ | 1797592593202151424 |
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| author | Victor Orlov Alexander Chichurin |
| author_facet | Victor Orlov Alexander Chichurin |
| author_sort | Victor Orlov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T01:53:25Z |
| format | Article |
| id | doaj.art-c221a76408834b10b3dc94b3d836b79e |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T01:53:25Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c221a76408834b10b3dc94b3d836b79e2023-11-18T12:50:51ZengMDPI AGSymmetry2073-89942023-06-01156120010.3390/sym15061200The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex DomainVictor Orlov0Alexander Chichurin1Institute of Digital Technologies and Modeling in Construction, Moscow State University of Civil Engineering, Yaroslavskoe Shosse, 26, Moscow 129337, RussiaDepartment of Mathematical Modeling, The John Paul II Catholic University of Lublin, ul. Konstantynów 1H, 20-708 Lublin, PolandIn 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.https://www.mdpi.com/2073-8994/15/6/1200nonlinear differential equation of the second ordermovable singular pointanalytical approximate solution |
| spellingShingle | Victor Orlov Alexander Chichurin 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 nonlinear differential equation of the second order movable singular point analytical approximate solution |
| title | The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain |
| title_full | The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain |
| title_fullStr | The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain |
| title_full_unstemmed | The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain |
| title_short | The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain |
| title_sort | influence of the perturbation of the initial data on the analytic approximate solution of the van der pol equation in the complex domain |
| topic | nonlinear differential equation of the second order movable singular point analytical approximate solution |
| url | https://www.mdpi.com/2073-8994/15/6/1200 |
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