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

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

Solving multi-point problem for Volterra-Fredholm integro-differential equations using Dzhumabaev parameterization method / Bakirova, Elmira A. (CC BY)

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fullscreen : Solving multi-point problem for Volterra-Fredholm integro-differential equations using Dzhumabaev parameterization method / Bakirova, Elmira A. (CC BY)

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Periodical

Title:: Open mathematics

Publication:: Berlin: de Gruyter

Note:: Gesehen am 21.04.15; Open Access; Namensnennung 4.0 International

Scope:: Online-Ressource

ISSN:: 2391-5455

ZDB-ID:: 2818690-4

VÖBB-Katalog:: 35275773

Previous Title:: Central European journal of mathematics

Keywords:: Zeitschrift

Classification:: Mathematik

Collection:: Mathematik

Copyright:: Rights reserved

Accessibility:: Free Access

Title:: Open mathematics

Publication:: Berlin: de Gruyter

Note:: Gesehen am 21.04.15; Open Access; Namensnennung 4.0 International

Scope:: Online-Ressource

ISSN:: 2391-5455

ZDB-ID:: 2818690-4

VÖBB-Katalog:: 35275773

Previous Title:: Central European journal of mathematics

Keywords:: Zeitschrift

Classification:: Mathematik

Collection:: Mathematik

Copyright:: Rights reserved

Accessibility:: Free Access

Article

Author:: Bakirova, Elmira A.; Assanova, Anar T.; Kadirbayeva, Zhazira M.

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

Publication:: Berlin: de Gruyter, 2024

Language:: English

Information:: 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.

Scope:: Online-Ressource

Note:: Open Access; Archivierung/Langzeitarchivierung gewährleistet

Keywords:: boundary value problem ; Volterra-Fredholm integro-differential equation ; parameterization method ; algorithm ; numerical solution ; 34K10 ; 34K28 ; 45J99

Classification:: Mathematik

URN:: urn:nbn:de:101:1-2408231613567.775395679870

Collection:: Mathematik

Copyright:: CC BY

Accessibility:: Free Access

Author:: Bakirova, Elmira A.; Assanova, Anar T.; Kadirbayeva, Zhazira M.

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

Publication:: Berlin: de Gruyter, 2024

Language:: English

Information:: 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.

Scope:: Online-Ressource

Note:: Open Access; Archivierung/Langzeitarchivierung gewährleistet

Keywords:: boundary value problem ; Volterra-Fredholm integro-differential equation ; parameterization method ; algorithm ; numerical solution ; 34K10 ; 34K28 ; 45J99

Classification:: Mathematik

URN:: urn:nbn:de:101:1-2408231613567.775395679870

Collection:: Mathematik

Copyright:: CC BY

Accessibility:: Free Access

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