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

Mathematics

卷:8

YoungIm Cho¹  Assiya Zhumanazarova¹ 

[1] Department of Computer Engineering, Gachon University, Gyeonggi-do 461-701, Korea;

关键词: small parameter;    singular perturbation;    boundary functions;    asymptotic estimates;   

DOI  :  10.3390/math8020213

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown