Boundary value problem for system of finite-difference with averaging equations

  • Sergey A. Spaskov Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus
  • Anton K. Khmyzov Epam Systems, 1/1 Akademika Kupreviča Street, Minsk 220141, Belarus

Abstract

The boundary value problem for the system of linear nonhomogeneous differential equations with generalized coefficients is considered X(t) = L(t)X(t) + F(t), M1X(0) + M2X(b) = Q, where t ∈ T = [0, b], L : T → Rpxp and F : T → Rp are right-continuous matrix and vector valued functions of bounded variation; M1, M2 ∈ Rpxp, Q ∈ Rp are defined matrices and vector. The problem is investigated with the help of the corresponding finite-difference with averaging equation behavior studying. The definition of the fundamental matrix, corresponding to the finite-difference with averaging equation is introduced. The theorem of the existence and uniqueness of the finite-difference with averaging boundary value problem, corresponding to the described system is proved.

Author Biographies

Sergey A. Spaskov, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

postgraduate student at the department of functional analysis and analytical economics, faculty of mechanics and mathematics

Anton K. Khmyzov, Epam Systems, 1/1 Akademika Kupreviča Street, Minsk 220141, Belarus

leading software engineer

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Published
2018-05-05
Keywords: system of linear nonhomogeneous differential equations, boundary value problem, finite-difference with averaging equations, fundamental matrix
How to Cite
Spaskov, S. A., & Khmyzov, A. K. (2018). Boundary value problem for system of finite-difference with averaging equations. Journal of the Belarusian State University. Mathematics and Informatics, 1, 17-28. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/882
Issue
No 1 (2018): Journal of the Belarusian State University. Mathematics and Informatics
Section
Differential Equations and Optimal Control

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