Implementation of the Adams method for solving ordinary differential equations in the Sage computer algebra system
This work is devoted to the implementation and testing of the Adams method for solving ordinary differential equations in the Sage computer algebra system. The Sage computer algebra system has, to some extent, trivial means for numerical integration of ordinary differential equations, but at the sam...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Peoples’ Friendship University of Russia (RUDN University)
2023-12-01
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| Series: | Discrete and Continuous Models and Applied Computational Science |
| Subjects: | |
| Online Access: | https://journals.rudn.ru/miph/article/viewFile/35112/22193 |
| _version_ | 1797789087967477760 |
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| author | Mikhail D. Malykh Polina S. Chusovitina |
| author_facet | Mikhail D. Malykh Polina S. Chusovitina |
| author_sort | Mikhail D. Malykh |
| collection | DOAJ |
| description | This work is devoted to the implementation and testing of the Adams method for solving ordinary differential equations in the Sage computer algebra system. The Sage computer algebra system has, to some extent, trivial means for numerical integration of ordinary differential equations, but at the same time, it is worth noting that this environment is convenient and practical for conducting computer experiments related to symbolic numerical calculations in it. The article presents the FDM package developed on the basis of the RUDN, which contains the developments of recent years, performed by M. D. Malykh and his students, for numerical integration of differential equations. In this package, attention is paid to the visualization of the calculation results, including the construction of various kinds of auxiliary diagrams, such as Richardson diagrams, as well as graphs of dependence, for example, the value of a function or step from a moment in time. The implementation of the Adams method will be considered from this package. In this article, this implementation of the Adams method will be tested on various examples of input data, and the method will also be compared with the Jacobi system. Exact and approximate values will be found and compared, and an estimate for the error will be obtained. |
| first_indexed | 2024-03-13T01:45:49Z |
| format | Article |
| id | doaj.art-8f809636ae6d47d68ef02484ed2a4266 |
| institution | Directory Open Access Journal |
| issn | 2658-4670 2658-7149 |
| language | English |
| last_indexed | 2024-03-13T01:45:49Z |
| publishDate | 2023-12-01 |
| publisher | Peoples’ Friendship University of Russia (RUDN University) |
| record_format | Article |
| series | Discrete and Continuous Models and Applied Computational Science |
| spelling | doaj.art-8f809636ae6d47d68ef02484ed2a42662023-07-03T08:28:11ZengPeoples’ Friendship University of Russia (RUDN University)Discrete and Continuous Models and Applied Computational Science2658-46702658-71492023-12-0131216417310.22363/2658-4670-2023-31-2-164-17321017Implementation of the Adams method for solving ordinary differential equations in the Sage computer algebra systemMikhail D. Malykh0https://orcid.org/0000-0001-6541-6603Polina S. Chusovitina1https://orcid.org/0009-0006-4191-2454RUDN UniversityRUDN UniversityThis work is devoted to the implementation and testing of the Adams method for solving ordinary differential equations in the Sage computer algebra system. The Sage computer algebra system has, to some extent, trivial means for numerical integration of ordinary differential equations, but at the same time, it is worth noting that this environment is convenient and practical for conducting computer experiments related to symbolic numerical calculations in it. The article presents the FDM package developed on the basis of the RUDN, which contains the developments of recent years, performed by M. D. Malykh and his students, for numerical integration of differential equations. In this package, attention is paid to the visualization of the calculation results, including the construction of various kinds of auxiliary diagrams, such as Richardson diagrams, as well as graphs of dependence, for example, the value of a function or step from a moment in time. The implementation of the Adams method will be considered from this package. In this article, this implementation of the Adams method will be tested on various examples of input data, and the method will also be compared with the Jacobi system. Exact and approximate values will be found and compared, and an estimate for the error will be obtained.https://journals.rudn.ru/miph/article/viewFile/35112/22193differential equationsadams methodsagefdm packagecauchy theoremtaylor seriesrichardson diagram |
| spellingShingle | Mikhail D. Malykh Polina S. Chusovitina Implementation of the Adams method for solving ordinary differential equations in the Sage computer algebra system Discrete and Continuous Models and Applied Computational Science differential equations adams method sage fdm package cauchy theorem taylor series richardson diagram |
| title | Implementation of the Adams method for solving ordinary differential equations in the Sage computer algebra system |
| title_full | Implementation of the Adams method for solving ordinary differential equations in the Sage computer algebra system |
| title_fullStr | Implementation of the Adams method for solving ordinary differential equations in the Sage computer algebra system |
| title_full_unstemmed | Implementation of the Adams method for solving ordinary differential equations in the Sage computer algebra system |
| title_short | Implementation of the Adams method for solving ordinary differential equations in the Sage computer algebra system |
| title_sort | implementation of the adams method for solving ordinary differential equations in the sage computer algebra system |
| topic | differential equations adams method sage fdm package cauchy theorem taylor series richardson diagram |
| url | https://journals.rudn.ru/miph/article/viewFile/35112/22193 |
| work_keys_str_mv | AT mikhaildmalykh implementationoftheadamsmethodforsolvingordinarydifferentialequationsinthesagecomputeralgebrasystem AT polinaschusovitina implementationoftheadamsmethodforsolvingordinarydifferentialequationsinthesagecomputeralgebrasystem |