Asymptotic estimates of the solution for a singularly perturbed Cauchy problem
The article focuses on the initial problem for a third-order linear integro-differential equation with a small parameter at the higher derivatives, assuming that the roots of the additional characteristic equation have opposite signs. This paper presents a fundamental set of solutions and initial f...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2025-06-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | https://mts.buketov.edu.kz/index.php/mathematics-vestnik/article/view/876 |
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| _version_ | 1849417428388282368 |
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| author | N.U. Bukanay A.E. Mirzakulova A.T. Assanova |
| author_facet | N.U. Bukanay A.E. Mirzakulova A.T. Assanova |
| author_sort | N.U. Bukanay |
| collection | DOAJ |
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The article focuses on the initial problem for a third-order linear integro-differential equation with a small parameter at the higher derivatives, assuming that the roots of the additional characteristic equation have opposite signs. This paper presents a fundamental set of solutions and initial functions for a singularly perturbed homogeneous differential equation. The solution to the singularly perturbed initial integrodifferential problem employs analytical formulas. A theorem concerning asymptotic estimates of the solution is established.
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| format | Article |
| id | doaj-art-1c40159170714b2ea54fe88a81f4faa4 |
| institution | Kabale University |
| issn | 2518-7929 2663-5011 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj-art-1c40159170714b2ea54fe88a81f4faa42025-08-20T03:32:51ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112025-06-01118210.31489/2025m2/44-51Asymptotic estimates of the solution for a singularly perturbed Cauchy problemN.U. Bukanay0https://orcid.org/0009-0009-2206-2302A.E. Mirzakulova1https://orcid.org/0000-0001-6445-6371A.T. Assanova2https://orcid.org/0000-0001-8697-8920al-Farabi Kazakh National University, Almaty, Kazakhstanal-Farabi Kazakh National University, Almaty, KazakhstanInstitute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan The article focuses on the initial problem for a third-order linear integro-differential equation with a small parameter at the higher derivatives, assuming that the roots of the additional characteristic equation have opposite signs. This paper presents a fundamental set of solutions and initial functions for a singularly perturbed homogeneous differential equation. The solution to the singularly perturbed initial integrodifferential problem employs analytical formulas. A theorem concerning asymptotic estimates of the solution is established. https://mts.buketov.edu.kz/index.php/mathematics-vestnik/article/view/876singularly perturbed integro-differential equationasymptotic estimatesCauchy functionsfundamental solutionssmall parameter |
| spellingShingle | N.U. Bukanay A.E. Mirzakulova A.T. Assanova Asymptotic estimates of the solution for a singularly perturbed Cauchy problem Қарағанды университетінің хабаршысы. Математика сериясы singularly perturbed integro-differential equation asymptotic estimates Cauchy functions fundamental solutions small parameter |
| title | Asymptotic estimates of the solution for a singularly perturbed Cauchy problem |
| title_full | Asymptotic estimates of the solution for a singularly perturbed Cauchy problem |
| title_fullStr | Asymptotic estimates of the solution for a singularly perturbed Cauchy problem |
| title_full_unstemmed | Asymptotic estimates of the solution for a singularly perturbed Cauchy problem |
| title_short | Asymptotic estimates of the solution for a singularly perturbed Cauchy problem |
| title_sort | asymptotic estimates of the solution for a singularly perturbed cauchy problem |
| topic | singularly perturbed integro-differential equation asymptotic estimates Cauchy functions fundamental solutions small parameter |
| url | https://mts.buketov.edu.kz/index.php/mathematics-vestnik/article/view/876 |
| work_keys_str_mv | AT nubukanay asymptoticestimatesofthesolutionforasingularlyperturbedcauchyproblem AT aemirzakulova asymptoticestimatesofthesolutionforasingularlyperturbedcauchyproblem AT atassanova asymptoticestimatesofthesolutionforasingularlyperturbedcauchyproblem |