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 fu...

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Bibliographic Details
Published inҚарағанды университетінің хабаршысы. Математика сериясы Vol. 118; no. 2; pp. 44 - 51
Main Authors Bukanay, N.U., Mirzakulova, A.E., Assanova, A.T.
Format Journal Article
LanguageEnglish
Published Academician Ye.A. Buketov Karaganda University 30.06.2025
Subjects
asymptotic estimates
Cauchy functions
fundamental solutions
singularly perturbed integro-differential equation
small parameter
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ISSN2518-7929
2663-5011
2663-5011
DOI10.31489/2025m2/44-51

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Summary: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.
ISSN:2518-7929
2663-5011
2663-5011
DOI:10.31489/2025m2/44-51