Solving multi-point problem for Volterra-Fredholm integro-differential equations using Dzhumabaev parameterization method-Reference-Cited by-同舟云学术

Solving multi-point problem for Volterra-Fredholm integro-differential equations using Dzhumabaev parameterization method

Published:2024-01-01 Issue:1 Volume:22 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Bakirova Elmira A.¹²,Assanova Anar T.¹,Kadirbayeva Zhazira M.¹²³

Affiliation:

1. Institute of Mathematics and Mathematical Modeling , Almaty , Kazakhstan

2. Kazakh National Women’s Teacher Training University , Almaty , Kazakhstan

3. International Information Technology University , Almaty , Kazakhstan

Abstract

Abstract In this study, a multipoint boundary value problem for Volterra-Fredholm integro-differential equations is considered. The addition of a new function converts the system of Volterra-Fredholm integro-differential equations to a system of Fredholm integro-differential equations. In contrast to the original problem, the dimension of a Fredholm integro-differential equation is determined by the number of matrices in the degenerate kernel of the Volterra integral. A numerical algorithm of Dzhumabaev parameterization method for addressing a multipoint boundary value problem for Volterra-Fredholm integro-differential equations is proposed. The main advantage of the proposed method is splitting the problem into auxiliary Cauchy problems for ordinary differential equations and a system of algebraic equations with respect to the parameters. The conditions for the unique solvability of the multipoint boundary value problem for Fredholm integro-differential equations are established. Finally, various numerical examples are provided to demonstrate the efficiency and correctness of the suggested technique.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/math-2024-0024/pdf

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