WSEAS Transactions on Systems and Control


Print ISSN: 1991-8763
E-ISSN: 2224-2856

Volume 12, 2017

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 12, 2017



Integral Boundary Value Problem for Second-Order Linear Integro-Differential Equations with a Small Parameter

AUTHORS: Kalimoldayev Maksat, Kalizhanova Аliya, Kozbakova Ainur, Kartbayev Timur, Aitkulov Zhalau, Abdildayeva Assel, Akhmetzhanov Maxat, Kopbosyn Leila

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ABSTRACT: This work is devoted to the asymptotic solutions of integral boundary value problem for the Interlinear second order differential equation of Fredholm type. Studying an integral boundary value task, obtaining solution assessment of the set singular perturbed integral boundary value problem and difference estimate between the solutions of singular perturbed and unperturbed tasks; determination of singular perturbed integral boundary value problem solution behavior mode and its derivatives in discontinuity (jump) of the considered section and determination of the solution initial jumps values at discontinuity and of an integral member of the equation, as well, creation of asymptotic solution expansion assessing a residual member with any range of accuracy according to a small parameter by means of Cauchy task with an initial jump, at that selection of initial conditions due to singular perturbed boundary value problem solution behavior mode and its derivatives in the jump point. In the paper there applied methods of differential and integral equations theories, boundary function method, method of successive approximations and method of mathematical induction

KEYWORDS: Singular, differential equations, asymptotic solutions, integral boundary problem, small parameter.

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WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 12, 2017, Art. #48, pp. 463-475


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