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A problem with parameter for the integro-differential equations

    Elmira A. Bakirova Affiliation
    ; Anar T. Assanova   Affiliation
    ; Zhazira M. Kadirbayeva Affiliation

Abstract

The article proposes a numerically approximate method for solving a boundary value problem for an integro-differential equation with a parameter and considers its convergence, stability, and accuracy. The integro-differential equation with a parameter is approximated by a loaded differential equation with a parameter. A new general solution to the loaded differential equation with a parameter is introduced and its properties are described. The solvability of the boundary value problem for the loaded differential equation with a parameter is reduced to the solvability of a system of linear algebraic equations with respect to arbitrary vectors of the introduced general solution. The coefficients and the right-hand sides of the system are compiled through solutions of the Cauchy problems for ordinary differential equations. Algorithms are proposed for solving the boundary value problem for the loaded differential equation with a parameter. The relationship between the qualitative properties of the initial and approximate problems is established, and estimates of the differences between their solutions are given.

Keyword : integro-differential equation, problem with parameter, δm(θ) general solution, solvability criteria, algorithm, numerical solution

How to Cite
Bakirova, E. A., Assanova, A. T., & Kadirbayeva, Z. M. (2021). A problem with parameter for the integro-differential equations. Mathematical Modelling and Analysis, 26(1), 34-54. https://doi.org/10.3846/mma.2021.11977
Published in Issue
Jan 18, 2021
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This work is licensed under a Creative Commons Attribution 4.0 International License.

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