Solving multi-point problem for Volterra-Fredholm integro-differential equations using Dzhumabaev parameterization method
Bakirova E.A. Assanova A.T. Kadirbayeva Z.M.
1 January 2024Walter de Gruyter GmbH
Open Mathematics
2024#22Issue 1
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.
algorithm , boundary value problem , numerical solution , parameterization method , Volterra-Fredholm integro-differential equation
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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Kazakh National Womens Teacher Training University, Almaty, Kazakhstan
International Information Technology University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Kazakh National Womens Teacher Training University
International Information Technology University
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