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Two-Point Boundary Value Problem for Volterra–Fredholm Integro-Differential Equations and Its Numerical Analysis

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Abstract

A two-point boundary value problem for Volterra–Fredholm integro-differential equations is considered. To solve this problem, Dzhumabaev parametrization method is used. Conditions for the existence and uniqueness of two-point boundary value problem for Volterra–Fredholm integro-differential equations are established. An algorithm for finding solution of this problem is proposed. Then, numerical approach for analysis of two-point boundary value problem for Volterra–Fredholm integro-differential equations is offered. Results are illustrated by numerical example.

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Funding

This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (grant no. AP09258829).

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Authors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, Department of Differential Equations, 050010/A26G7T4, Almaty, Kazakhstan

    A. T. Assanova, E. A. Bakirova & Zh. M. Kadirbayeva

  2. Kazakh National Women’s Teacher Training University, 050026/A05M0T6, Almaty, Kazakhstan

    A. T. Assanova & E. A. Bakirova

  3. International Information Technology University, Department of Mathematical and Computer Modeling, 050040/A15M0F0, Almaty, Kazakhstan

    Zh. M. Kadirbayeva

Authors
  1. A. T. Assanova
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  2. E. A. Bakirova
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  3. Zh. M. Kadirbayeva
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Corresponding authors

Correspondence to A. T. Assanova, E. A. Bakirova or Zh. M. Kadirbayeva.

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(Submitted by T. K. Yuldashev)

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Assanova, A.T., Bakirova, E.A. & Kadirbayeva, Z.M. Two-Point Boundary Value Problem for Volterra–Fredholm Integro-Differential Equations and Its Numerical Analysis. Lobachevskii J Math 44, 1100–1110 (2023). https://doi.org/10.1134/S1995080223030058

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  • DOI: https://doi.org/10.1134/S1995080223030058

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