Singularly Perturbed Boundary Value Problem with Multizonal Interior Transitional Layer
Two-point boundary value problem for a singularly perturbed ordinary differential equation of second order is considered in the case when the degenerate equation has three unintersecting roots from which one root is two-tuple and two roots are one-tuple. It is prooved that for sufficiently small val...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2015-02-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/228 |
| _version_ | 1797877877574729728 |
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| author | V. F. Butuzov |
| author_facet | V. F. Butuzov |
| author_sort | V. F. Butuzov |
| collection | DOAJ |
| description | Two-point boundary value problem for a singularly perturbed ordinary differential equation of second order is considered in the case when the degenerate equation has three unintersecting roots from which one root is two-tuple and two roots are one-tuple. It is prooved that for sufficiently small values of the small parameter the problem has a solution with the transition from the two-tuple root of the degenerate equation to the one-tuple root in the neighbourhood of an internal point of the interval. The asymptotic expansion of this solution is constructed. It distinguishes from the known expansion in the case when all roots of the degenerate equation are one-tuple, in particular, the transitional layer is multizonal. |
| first_indexed | 2024-04-10T02:24:54Z |
| format | Article |
| id | doaj.art-6afc5c2555e04660a99104dc5ccd5b7a |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-10T02:24:54Z |
| publishDate | 2015-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-6afc5c2555e04660a99104dc5ccd5b7a2023-03-13T08:07:33ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-02-0122152210.18255/1818-1015-2015-1-5-22221Singularly Perturbed Boundary Value Problem with Multizonal Interior Transitional LayerV. F. Butuzov0Московский государственный университет им. М.В. ЛомоносоваTwo-point boundary value problem for a singularly perturbed ordinary differential equation of second order is considered in the case when the degenerate equation has three unintersecting roots from which one root is two-tuple and two roots are one-tuple. It is prooved that for sufficiently small values of the small parameter the problem has a solution with the transition from the two-tuple root of the degenerate equation to the one-tuple root in the neighbourhood of an internal point of the interval. The asymptotic expansion of this solution is constructed. It distinguishes from the known expansion in the case when all roots of the degenerate equation are one-tuple, in particular, the transitional layer is multizonal.https://www.mais-journal.ru/jour/article/view/228сингулярно возмущённое уравнениевнутренний переходный слойасимптотическое разложение решения |
| spellingShingle | V. F. Butuzov Singularly Perturbed Boundary Value Problem with Multizonal Interior Transitional Layer Моделирование и анализ информационных систем сингулярно возмущённое уравнение внутренний переходный слой асимптотическое разложение решения |
| title | Singularly Perturbed Boundary Value Problem with Multizonal Interior Transitional Layer |
| title_full | Singularly Perturbed Boundary Value Problem with Multizonal Interior Transitional Layer |
| title_fullStr | Singularly Perturbed Boundary Value Problem with Multizonal Interior Transitional Layer |
| title_full_unstemmed | Singularly Perturbed Boundary Value Problem with Multizonal Interior Transitional Layer |
| title_short | Singularly Perturbed Boundary Value Problem with Multizonal Interior Transitional Layer |
| title_sort | singularly perturbed boundary value problem with multizonal interior transitional layer |
| topic | сингулярно возмущённое уравнение внутренний переходный слой асимптотическое разложение решения |
| url | https://www.mais-journal.ru/jour/article/view/228 |
| work_keys_str_mv | AT vfbutuzov singularlyperturbedboundaryvalueproblemwithmultizonalinteriortransitionallayer |