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Article · BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS · June 30, 2025
Asymptotic estimates of the solution for a singularly perturbed Cauchy problem
N.U. Bukanay, A. E. Mirzakulova, A. T. Assanova
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.
Differential Equations and Numerical MethodsDifferential Equations and Boundary ProblemsNonlinear Differential Equations Analysissingularly perturbed problemsCauchy problemintegro-differential equations
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