Asymptotic Expansions of Eigenvalues of the First Boundary Problem for Singularly Perturbed Second Order Differential Equation with Turning Points
For singularly perturbed second order equations the dependence of eigenvalues of the first boundary problem on a small parameter at the highest derivative is studied. The main assumption is that the coefficient at the first derivative in the equation is the sign of the variable. This leads to the emergi...
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Yaroslavl State University
2016-02-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/305 |
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| author | S. A. Kashchenko |
| author_facet | S. A. Kashchenko |
| author_sort | S. A. Kashchenko |
| collection | DOAJ |
| description | For singularly perturbed second order equations the dependence of eigenvalues of the first boundary problem on a small parameter at the highest derivative is studied. The main assumption is that the coefficient at the first derivative in the equation is the sign of the variable. This leads to the emerging of so-called turning points. Asymptotic expansions on the small parameter are obtained for all eigenvalues of the considered boundary problem. It turns out that the expansions are defined by the behavior of coefficients in a neighborhood of turning points only |
| format | Article |
| id | doaj-art-d5db75e5f9df4948b81636e284d0de55 |
| institution | DOAJ |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2016-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-d5db75e5f9df4948b81636e284d0de552025-08-20T03:01:13ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172016-02-01231416010.18255/1818-1015-2016-1-41-60281Asymptotic Expansions of Eigenvalues of the First Boundary Problem for Singularly Perturbed Second Order Differential Equation with Turning PointsS. A. Kashchenko0P.G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, RussiaFor singularly perturbed second order equations the dependence of eigenvalues of the first boundary problem on a small parameter at the highest derivative is studied. The main assumption is that the coefficient at the first derivative in the equation is the sign of the variable. This leads to the emerging of so-called turning points. Asymptotic expansions on the small parameter are obtained for all eigenvalues of the considered boundary problem. It turns out that the expansions are defined by the behavior of coefficients in a neighborhood of turning points onlyhttps://www.mais-journal.ru/jour/article/view/305singularly perturbed equationturning pointsasymptoticboundary value problemeigenvalues |
| spellingShingle | S. A. Kashchenko Asymptotic Expansions of Eigenvalues of the First Boundary Problem for Singularly Perturbed Second Order Differential Equation with Turning Points Моделирование и анализ информационных систем singularly perturbed equation turning points asymptotic boundary value problem eigenvalues |
| title | Asymptotic Expansions of Eigenvalues of the First Boundary Problem for Singularly Perturbed Second Order Differential Equation with Turning Points |
| title_full | Asymptotic Expansions of Eigenvalues of the First Boundary Problem for Singularly Perturbed Second Order Differential Equation with Turning Points |
| title_fullStr | Asymptotic Expansions of Eigenvalues of the First Boundary Problem for Singularly Perturbed Second Order Differential Equation with Turning Points |
| title_full_unstemmed | Asymptotic Expansions of Eigenvalues of the First Boundary Problem for Singularly Perturbed Second Order Differential Equation with Turning Points |
| title_short | Asymptotic Expansions of Eigenvalues of the First Boundary Problem for Singularly Perturbed Second Order Differential Equation with Turning Points |
| title_sort | asymptotic expansions of eigenvalues of the first boundary problem for singularly perturbed second order differential equation with turning points |
| topic | singularly perturbed equation turning points asymptotic boundary value problem eigenvalues |
| url | https://www.mais-journal.ru/jour/article/view/305 |
| work_keys_str_mv | AT sakashchenko asymptoticexpansionsofeigenvaluesofthefirstboundaryproblemforsingularlyperturbedsecondorderdifferentialequationwithturningpoints |