On application of solution continuation method with respect to the best exponential argument in solving stiff boundary value problems
The problematic of solving stiff boundary value problems permeates numerous scientific and engineering disciplines, demanding novel approaches to surpass the limitations of traditional numerical techniques. This research delves into the implementation of the solution continuation method with respect...
| 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/37517/23060 |
| _version_ | 1797349202043338752 |
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| author | Ekaterina D. Tsapko Sergey S. Leonov Evgenii B. Kuznetsov |
| author_facet | Ekaterina D. Tsapko Sergey S. Leonov Evgenii B. Kuznetsov |
| author_sort | Ekaterina D. Tsapko |
| collection | DOAJ |
| description | The problematic of solving stiff boundary value problems permeates numerous scientific and engineering disciplines, demanding novel approaches to surpass the limitations of traditional numerical techniques. This research delves into the implementation of the solution continuation method with respect to the best exponential argument, to address these stiff problems characterized by rapidly evolving integral curves. The investigation was conducted by comparing the efficiency and stability of this novel method against the conventional shooting method, which has been a cornerstone in addressing such problems but struggles with the erratic growth of integral curves. The results indicate a marked elevation in computational efficiency when the problem is transformed using the exponential best argument. This method is particularly pronounced in scenarios where integral curves exhibit exponential growth speed. The main takeaway from this study is the instrumental role of the regularization parameter. Its judicious selection based on the unique attributes of the problem can dictate the efficiency of the solution. In summary, this research not only offers an innovative method to solve stiff boundary value problems but also underscores the nuances involved in method selection, potentially paving the way for further refinements and applications in diverse domains. |
| first_indexed | 2024-03-08T12:25:52Z |
| format | Article |
| id | doaj.art-0f4800e05699446fb8858eac54e46051 |
| institution | Directory Open Access Journal |
| issn | 2658-4670 2658-7149 |
| language | English |
| last_indexed | 2024-03-08T12:25:52Z |
| 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-0f4800e05699446fb8858eac54e460512024-01-22T08:09:08ZengPeoples’ Friendship University of Russia (RUDN University)Discrete and Continuous Models and Applied Computational Science2658-46702658-71492023-12-0131437538610.22363/2658-4670-2023-31-4-375-38621030On application of solution continuation method with respect to the best exponential argument in solving stiff boundary value problemsEkaterina D. Tsapko0https://orcid.org/0000-0002-4215-3510Sergey S. Leonov1https://orcid.org/0000-0001-6077-0435Evgenii B. Kuznetsov2https://orcid.org/0000-0002-9452-6577Joint Stock Company “Interregional Energy Service Company ‘Energoefficiency Technologies’ ”RUDN UniversityMoscow Aviation InstituteThe problematic of solving stiff boundary value problems permeates numerous scientific and engineering disciplines, demanding novel approaches to surpass the limitations of traditional numerical techniques. This research delves into the implementation of the solution continuation method with respect to the best exponential argument, to address these stiff problems characterized by rapidly evolving integral curves. The investigation was conducted by comparing the efficiency and stability of this novel method against the conventional shooting method, which has been a cornerstone in addressing such problems but struggles with the erratic growth of integral curves. The results indicate a marked elevation in computational efficiency when the problem is transformed using the exponential best argument. This method is particularly pronounced in scenarios where integral curves exhibit exponential growth speed. The main takeaway from this study is the instrumental role of the regularization parameter. Its judicious selection based on the unique attributes of the problem can dictate the efficiency of the solution. In summary, this research not only offers an innovative method to solve stiff boundary value problems but also underscores the nuances involved in method selection, potentially paving the way for further refinements and applications in diverse domains.https://journals.rudn.ru/miph/article/viewFile/37517/23060stiff boundary value problemssolution continuation methodthe best exponential argumentnumerical method stabilityintegral curvescomputational efficiencyshooting methodabsolute stability region |
| spellingShingle | Ekaterina D. Tsapko Sergey S. Leonov Evgenii B. Kuznetsov On application of solution continuation method with respect to the best exponential argument in solving stiff boundary value problems Discrete and Continuous Models and Applied Computational Science stiff boundary value problems solution continuation method the best exponential argument numerical method stability integral curves computational efficiency shooting method absolute stability region |
| title | On application of solution continuation method with respect to the best exponential argument in solving stiff boundary value problems |
| title_full | On application of solution continuation method with respect to the best exponential argument in solving stiff boundary value problems |
| title_fullStr | On application of solution continuation method with respect to the best exponential argument in solving stiff boundary value problems |
| title_full_unstemmed | On application of solution continuation method with respect to the best exponential argument in solving stiff boundary value problems |
| title_short | On application of solution continuation method with respect to the best exponential argument in solving stiff boundary value problems |
| title_sort | on application of solution continuation method with respect to the best exponential argument in solving stiff boundary value problems |
| topic | stiff boundary value problems solution continuation method the best exponential argument numerical method stability integral curves computational efficiency shooting method absolute stability region |
| url | https://journals.rudn.ru/miph/article/viewFile/37517/23060 |
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