A Solution to a Linear Boundary Value Problem for an Impulsive Integro-Differential Equation

Mynbayeva S. Assanova A. Uteshova R.
January 2026 Springer

Differential Equations and Dynamical Systems
2026 #34 Issue 1 9 - 29 pp.

This study deals with a boundary value problem for a linear Fredholm integro-differential equation subject to impulse effects at fixed time points. The interval is partitioned which that the set of partition points contains the points of impulse and the values of the desired function at the left-end points of the subintervals are introduced as parameters. Solving boundary value problem for the linear Fredholm integro-differential equation with impulsive inputs is reduced to the solving a system of linear algebraic equations with respect to the arbitrary parameters introduced. Solvability criteria of the problem are provided in terms of input data, without the use of a fundamental matrix and a resolvent of auxiliary integral equation. We also propose an algorithm to solve the problem under consideration, establish its convergence conditions, and provide a numerical version of the algorithm.

Impulsive integro-differential equations , Linear boundary value problem , Parametrization method , Solvability conditions

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Department of Mathematics, K.Zhubanov Aktobe Regional University, Moldagulova Ave., 34, Aktobe, 030000, Kazakhstan
Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, Pushkin Str., 125, Almaty, 050010, Kazakhstan
Department of Mathematical and Computer modeling, International IT University, Dzhandossov Str., 34A, Almaty, 050034, Kazakhstan

Department of Mathematics
Department of Differential Equations
Department of Mathematical and Computer modeling

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