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Inverse Problem for the Integral Dynamic Models with Discontinuous Kernels

Author

Listed:
  • Aleksandr N. Tynda

    (Department of Mathematics, Penza State University, Krasnaya Str., 40, 440026 Penza, Russia)

  • Denis N. Sidorov

    (Department of Applied Mathematics, Energy Systems Institute of Siberian Branch of Russian Academy of Science, 664033 Irkutsk, Russia
    Industrial Maths Lab., Baikal School of BRICS, Irkutsk National Research Technical University, 664088 Irkursk, Russia)

Abstract

The objective of this paper was to present a new inverse problem statement and numerical method for the Volterra integral equations with piecewise continuous kernels. For such Volterra integral equations of the first kind, it is assumed that kernel discontinuity curves are the desired ones, but the rest of the information is known. The resulting integral equation is nonlinear with respect to discontinuity curves which correspond to integration bounds. A direct method of discretization with a posteriori verification of calculations is proposed. The family of quadrature rules is employed for approximation purposes. It is shown that the arithmetic complexity of the proposed numerical method is O ( N 3 ) . The method has first-order convergence. A generalization of the method is also proposed for the case of an arbitrary number of discontinuity curves. The illustrative examples are included to demonstrate the efficiency and accuracy of proposed solver.

Suggested Citation

  • Aleksandr N. Tynda & Denis N. Sidorov, 2022. "Inverse Problem for the Integral Dynamic Models with Discontinuous Kernels," Mathematics, MDPI, vol. 10(21), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:3945-:d:951580
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    References listed on IDEAS

    as
    1. Denis Sidorov & Aleksandr Tynda & Ildar Muftahov & Aliona Dreglea & Fang Liu, 2020. "Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation," Mathematics, MDPI, vol. 8(8), pages 1-19, August.
    2. Denis Sidorov & Daniil Panasetsky & Nikita Tomin & Dmitriy Karamov & Aleksei Zhukov & Ildar Muftahov & Aliona Dreglea & Fang Liu & Yong Li, 2020. "Toward Zero-Emission Hybrid AC/DC Power Systems with Renewable Energy Sources and Storages: A Case Study from Lake Baikal Region," Energies, MDPI, vol. 13(5), pages 1-18, March.
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