| Issue |
E3S Web Conf.
Volume 164, 2020
Topical Problems of Green Architecture, Civil and Environmental Engineering 2019 (TPACEE 2019)
|
|
|---|---|---|
| Article Number | 09022 | |
| Number of page(s) | 9 | |
| Section | Environmental and Resource Economics | |
| DOI | https://doi.org/10.1051/e3sconf/202016409022 | |
| Published online | 05 May 2020 | |
Asymptotic methods for solving boundary value eigenvalue problems
Financial University under the Government of the Russian Federation, 125993, Leningradskiy Avenue, 49, Moscow, Russian Federation
* Corresponding author : galsevzhukova@mail.ru
The aim of the study is an approximate construction with a given accuracy of solutions of boundary value problems for eigenvalues under various types of boundary conditions. It is shown that the problem of finding approximate large eigenvalues of boundary value problems is reduced to the analysis and solution of singularly perturbed differential equations with variable coefficients. Methods used: asymptotic diagram method developed to construct the asymptotic behavior of solutions of singularly perturbed differential equations and systems; methods of numerical integration of boundary value problems. The main results obtained are: the asymptotics of the required accuracy are constructed in the analytical form for the eigenvalues and eigenfunctions of the boundary value problems under various boundary conditions; analysis of the computational capabilities of the practical use of the constructed asymptotics in comparison with the results of numerical integration.
© The Authors, published by EDP Sciences 2020
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