Asymptotic estimates of the solution for a singularly perturbed Cauchy problem

Authors

DOI:

https://doi.org/10.31489/2025m2/44-51

Keywords:

singularly perturbed integro-differential equation, asymptotic estimates, Cauchy functions, fundamental solutions, small parameter

Abstract

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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Published

2025-06-30

How to Cite

Bukanay, N., Mirzakulova, A., & Assanova, A. (2025). Asymptotic estimates of the solution for a singularly perturbed Cauchy problem. Bulletin of the Karaganda University. Mathematics Series, 118(2), 44–51. https://doi.org/10.31489/2025m2/44-51

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Section

MATHEMATICS