The Maximum Domain for an Analytical Approximate Solution to a Nonlinear Differential Equation in the Neighborhood of a Moving Singular Point
This paper presents the final stage in the study of the analytical approximate solution to a class of nonlinear differential equations unsolvable in quadrature in the general case in the neighborhood of a perturbed value of a moving singular point. An a priori error estimation is proven. The scope o...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/9/844 |
| _version_ | 1827727242436804608 |
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| author | Victor Orlov Magomedyusuf Gasanov |
| author_facet | Victor Orlov Magomedyusuf Gasanov |
| author_sort | Victor Orlov |
| collection | DOAJ |
| description | This paper presents the final stage in the study of the analytical approximate solution to a class of nonlinear differential equations unsolvable in quadrature in the general case in the neighborhood of a perturbed value of a moving singular point. An a priori error estimation is proven. The scope of application of the analytical approximate solution is extended; the formula for calculating this scope is obtained. The proof of the theorem is based on the application of elements of differential calculus. Theoretical results are supported by numerical calculations, which validate their reliability. The authors report a numerical comparison between the results, obtained in the paper, and the findings that were published earlier. |
| first_indexed | 2024-03-10T23:02:47Z |
| format | Article |
| id | doaj.art-a7160811c65a4137b526906a7244e1d6 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T23:02:47Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-a7160811c65a4137b526906a7244e1d62023-11-19T09:32:30ZengMDPI AGAxioms2075-16802023-08-0112984410.3390/axioms12090844The Maximum Domain for an Analytical Approximate Solution to a Nonlinear Differential Equation in the Neighborhood of a Moving Singular PointVictor Orlov0Magomedyusuf Gasanov1Institute of Digital Technologies and Modeling in Construction, Moscow State University of Civil Engineering, Yaroslavskoye Shosse, 26, 129337 Moscow, RussiaInstitute of Digital Technologies and Modeling in Construction, Moscow State University of Civil Engineering, Yaroslavskoye Shosse, 26, 129337 Moscow, RussiaThis paper presents the final stage in the study of the analytical approximate solution to a class of nonlinear differential equations unsolvable in quadrature in the general case in the neighborhood of a perturbed value of a moving singular point. An a priori error estimation is proven. The scope of application of the analytical approximate solution is extended; the formula for calculating this scope is obtained. The proof of the theorem is based on the application of elements of differential calculus. Theoretical results are supported by numerical calculations, which validate their reliability. The authors report a numerical comparison between the results, obtained in the paper, and the findings that were published earlier.https://www.mdpi.com/2075-1680/12/9/844nonlinearity aspectperturbation of a moving singular pointscope of applicationa priori estimation |
| spellingShingle | Victor Orlov Magomedyusuf Gasanov The Maximum Domain for an Analytical Approximate Solution to a Nonlinear Differential Equation in the Neighborhood of a Moving Singular Point Axioms nonlinearity aspect perturbation of a moving singular point scope of application a priori estimation |
| title | The Maximum Domain for an Analytical Approximate Solution to a Nonlinear Differential Equation in the Neighborhood of a Moving Singular Point |
| title_full | The Maximum Domain for an Analytical Approximate Solution to a Nonlinear Differential Equation in the Neighborhood of a Moving Singular Point |
| title_fullStr | The Maximum Domain for an Analytical Approximate Solution to a Nonlinear Differential Equation in the Neighborhood of a Moving Singular Point |
| title_full_unstemmed | The Maximum Domain for an Analytical Approximate Solution to a Nonlinear Differential Equation in the Neighborhood of a Moving Singular Point |
| title_short | The Maximum Domain for an Analytical Approximate Solution to a Nonlinear Differential Equation in the Neighborhood of a Moving Singular Point |
| title_sort | maximum domain for an analytical approximate solution to a nonlinear differential equation in the neighborhood of a moving singular point |
| topic | nonlinearity aspect perturbation of a moving singular point scope of application a priori estimation |
| url | https://www.mdpi.com/2075-1680/12/9/844 |
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