arXiv subjects

Anar Assanova

Publications and source records attributed to Anar Assanova.

3 recordsLinked to original sources

arXiv2026

Boundary value problems for linear differential-algebraic equations: solvability via the Kronecker canonical form

The solvability of two-point boundary value problems for constant-coefficient differential-algebraic equations is investigated. Unlike previous studies, which often assume that the matrix pair associated with the equation is regular, we consider the general singular case. Using the Kronecker canonical form, we decompose the problem into simpler subsystems, enabling a systematic analysis of solvability. The method of parameterization reduces the boundary value problem to a system of algebraic equations. We derive criteria for the existence and uniqueness of solutions and provide a comprehensive framework for solving such boundary value problems. Several illustrative examples are presented and show the applicability of the results.

math.CA↗

arXiv2023

Novel approach for solving multipoint boundary value problem for integro-differential equation

In the present paper, we study a multipoint boundary value problem for a system of Fredholm integro-differenial equations by the method of parameterization. The case of a degenerate kernel is studied separately, for which we obtain well-posedness conditions and propose some algorithms to find approximate and numerical solutions to the problem. Then we establish necessary and sufficient conditions for the well-posedness of the multipoint problem for the system of Fredholm integro-differential equations and develop some algorithms for finding its approximate solutions. These algorithms are based on the solutions of an approximating problem for the system of integro-differential equations with degenerate kernel.

math.NA↗

arXiv2023

On the solvability of boundary value problems for linear differential-algebraic equations with constant coefficients

We study a two-point boundary value problem for a linear differen\-tial-algebraic equation with constant coefficients by using the method of parameterization. The parameter is set as the value of the continuously differentiable component of the solution at the left endpoint of the interval. Applying the Weierstrass canonical form to the matrix pair associated with the differential-algebraic equation, we obtain a criterion for the unique solvability of the problem.

math.CA↗