SINGULARLY PERTURBED DIRIСHLET PROBLEM WITH A SINGULAR POINT
DOI:
https://doi.org/10.52754/16948610_2024_2_35Keywords:
Dirichlet problem, ordinary differential equation, singularly perturbed, boundary layer, maximum principle, singular pointAbstract
In many fields of science, complex problems are described by differential equations with small parameters. A famous physicist is credited with the phrase: "A phenomenon is not physical if it lacks a small parameter." Differential equations (ordinary or partial derivatives) with a small parameter at the highest derivative are called singularly perturbed. Such equations arise in electrical and radio engineering, mechanics, hydro and aerodynamics, etc. The article is devoted to the construction of the asymptotics of solving the singularly perturbed Dirichlet problem with a singularly point. First, an asymptotic expansion of the solution of the problem is constructed over the entire interval, then the residual term of this expansion is estimated.
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Бекмурза Уулу, Ы. Өзгөчө чекитке ээ болгон сингулярдык козголгон чектик маселенин чыгарылышынын асимптотикасы / Ы. Бекмурза Уулу // Вестник Ошского государственного университета. – 2023. – No. 4. – P. 87-95. – DOI: 10.52754/16948610_2023_4_10. – EDN: DQLNIP. DOI: https://doi.org/10.52754/16948610_2023_4_10
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