Reference modeling as a method for solving nonlinear problems
In this paper, the method of reference modeling is considered, designed for calculation, analysis and mathematical modeling of nonlinear physical phenomena and technological processes. The advantages of this method, the possibility of its application in the entire range of basic parameters of a nonl...
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| Format: | Article |
| Language: | Russian |
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North-Caucasus Federal University
2023-09-01
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| Series: | Современная наука и инновации |
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| Online Access: | https://msi.elpub.ru/jour/article/view/1475 |
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| author | A. B. Cheboksarov N. Yu. Botvineva V. A. Cheboksarov E. V. Polovinko |
| author_facet | A. B. Cheboksarov N. Yu. Botvineva V. A. Cheboksarov E. V. Polovinko |
| author_sort | A. B. Cheboksarov |
| collection | DOAJ |
| description | In this paper, the method of reference modeling is considered, designed for calculation, analysis and mathematical modeling of nonlinear physical phenomena and technological processes. The advantages of this method, the possibility of its application in the entire range of basic parameters of a nonlinear problem, the uniformity of the design scheme for all types of problems are formulated. The proposed method is used to create models of convective diffusion in an inhomogeneous medium, scattering of thermal electrons in a field with central symmetry, and the behavior of electrical conductivity depending on temperature and dielectric permittivity of wide-band semiconductors. The problem of calculating the transparency of a potential barrier that a particle hits, considered as a test, gave a good result (an error in the range of 0.8-1.2%). In this paper, the main features of using the reference modeling method for solving nonlinear differential equations are demonstrated. The obtained results of analysis and modeling allow us to confidently assess the reliability of the general ideas of the reference modeling method, its design scheme, as well as the convergence of its decompositions, the similarity criteria of the system under study and the selected model. The method proposed in this paper, taking into account its approbation in various conditions, can serve as a basis for application in the study of nonlinear problems of various nature, finding approximate solutions to nonlinear differential equations. |
| format | Article |
| id | doaj-art-9af0cdb8a6fa4e6fa2e5a5ea10058e6e |
| institution | Kabale University |
| issn | 2307-910X |
| language | Russian |
| publishDate | 2023-09-01 |
| publisher | North-Caucasus Federal University |
| record_format | Article |
| series | Современная наука и инновации |
| spelling | doaj-art-9af0cdb8a6fa4e6fa2e5a5ea10058e6e2025-08-20T03:42:21ZrusNorth-Caucasus Federal UniversityСовременная наука и инновации2307-910X2023-09-0102203210.37493/2307-910X.2023.2.21461Reference modeling as a method for solving nonlinear problemsA. B. Cheboksarov0N. Yu. Botvineva1V. A. Cheboksarov2E. V. Polovinko3Stavropol State Pedagogical Institute, Branch in EssentukiStavropol State Pedagogical Institute, Branch in EssentukiPyatigorsk Institute (branch) of North-Caucasus Federal UniversityPyatigorsk Institute (branch) of North-Caucasus Federal UniversityIn this paper, the method of reference modeling is considered, designed for calculation, analysis and mathematical modeling of nonlinear physical phenomena and technological processes. The advantages of this method, the possibility of its application in the entire range of basic parameters of a nonlinear problem, the uniformity of the design scheme for all types of problems are formulated. The proposed method is used to create models of convective diffusion in an inhomogeneous medium, scattering of thermal electrons in a field with central symmetry, and the behavior of electrical conductivity depending on temperature and dielectric permittivity of wide-band semiconductors. The problem of calculating the transparency of a potential barrier that a particle hits, considered as a test, gave a good result (an error in the range of 0.8-1.2%). In this paper, the main features of using the reference modeling method for solving nonlinear differential equations are demonstrated. The obtained results of analysis and modeling allow us to confidently assess the reliability of the general ideas of the reference modeling method, its design scheme, as well as the convergence of its decompositions, the similarity criteria of the system under study and the selected model. The method proposed in this paper, taking into account its approbation in various conditions, can serve as a basis for application in the study of nonlinear problems of various nature, finding approximate solutions to nonlinear differential equations.https://msi.elpub.ru/jour/article/view/1475mathematical modelingnonlinear differential equationsthe method of reference modeling |
| spellingShingle | A. B. Cheboksarov N. Yu. Botvineva V. A. Cheboksarov E. V. Polovinko Reference modeling as a method for solving nonlinear problems Современная наука и инновации mathematical modeling nonlinear differential equations the method of reference modeling |
| title | Reference modeling as a method for solving nonlinear problems |
| title_full | Reference modeling as a method for solving nonlinear problems |
| title_fullStr | Reference modeling as a method for solving nonlinear problems |
| title_full_unstemmed | Reference modeling as a method for solving nonlinear problems |
| title_short | Reference modeling as a method for solving nonlinear problems |
| title_sort | reference modeling as a method for solving nonlinear problems |
| topic | mathematical modeling nonlinear differential equations the method of reference modeling |
| url | https://msi.elpub.ru/jour/article/view/1475 |
| work_keys_str_mv | AT abcheboksarov referencemodelingasamethodforsolvingnonlinearproblems AT nyubotvineva referencemodelingasamethodforsolvingnonlinearproblems AT vacheboksarov referencemodelingasamethodforsolvingnonlinearproblems AT evpolovinko referencemodelingasamethodforsolvingnonlinearproblems |