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Asymptotic Convergence of the Solution of a Singularly Perturbed Integro-Differential Boundary Value Problem

Department of Computer Engineering, Gachon University, Gyeonggi-do 461-701, Korea
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Mathematics 2020, 8(2), 213; https://doi.org/10.3390/math8020213
Received: 3 January 2020 / Revised: 4 February 2020 / Accepted: 6 February 2020 / Published: 7 February 2020
In this study, the asymptotic behavior of the solutions to a boundary value problem for a third-order linear integro-differential equation with a small parameter at the two higher derivatives has been examined, under the condition that the roots of the additional characteristic equation are negative. Via the scheme of methods and algorithms pertaining to the qualitative study of singularly perturbed problems with initial jumps, a fundamental system of solutions, the Cauchy function, and the boundary functions of a homogeneous singularly perturbed differential equation are constructed. Analytical formulae for the solutions and asymptotic estimates of the singularly perturbed problem are obtained. Furthermore, a modified degenerate boundary value problem has been constructed, and it was stated that the solution of the original singularly perturbed boundary value problem tends to this modified problem’s solution.
Keywords: small parameter; singular perturbation; boundary functions; asymptotic estimates small parameter; singular perturbation; boundary functions; asymptotic estimates
MDPI and ACS Style

Zhumanazarova, A.; Cho, Y.I. Asymptotic Convergence of the Solution of a Singularly Perturbed Integro-Differential Boundary Value Problem. Mathematics 2020, 8, 213.

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