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Methods for Calculating a Mathematical Model for Determining the Electromagnetic Field in Conducting Ferromagnetic Layer

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Advances in Intelligent Systems and Computing V (CSIT 2020)

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Abstract

The values of magnetic and electric field voltages during induction heating of an electrically conductive ferromagnetic layer in a stationary time periodic electromagnetic field are investigated. The problem is solved using a method of small parameter and embedded methods of the Runge-Kutta type with a two-sided estimate of the local error. The proposed formulas, using only three calls to the right side of the differential equation, make it possible to obtain at each nodal point not only second and third order accuracy methods and two-sided first and second order accuracy formulas, but also the estimation of the principal terms of the local error of the two-sided approximations. Numerical calculations have shown a significant effect on the distribution of the amplitudes of the harmonics of the field strength of the nonlinear relationship between induction and magnetic field strength.

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Authors and Affiliations

  1. Department of Computational Mathematics and Programming, Lviv Polytechnic National University, Lviv, Ukraine

    Yaroslav Pelekh, Andrii Kunynets, Serhii Mentynskyi & Bohdan Fil

  2. Department of Artificial Intelligent Systems, Lviv Polytechnic National University, Lviv, Ukraine

    Pavlo Pukach

Authors
  1. Yaroslav Pelekh
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  2. Andrii Kunynets
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  3. Serhii Mentynskyi
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  4. Bohdan Fil
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  5. Pavlo Pukach
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Corresponding author

Correspondence to Yaroslav Pelekh .

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Editors and Affiliations

  1. Department of Artificial Intelligence, Lviv Polytechnic National University, Lviv, Ukraine

    Natalya Shakhovska

  2. Institute of Computer Science and Information Technologies, Lviv Polytechnic National University, Lviv, Ukraine

    Mykola O. Medykovskyy

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Pelekh, Y., Kunynets, A., Mentynskyi, S., Fil, B., Pukach, P. (2021). Methods for Calculating a Mathematical Model for Determining the Electromagnetic Field in Conducting Ferromagnetic Layer. In: Shakhovska, N., Medykovskyy, M.O. (eds) Advances in Intelligent Systems and Computing V. CSIT 2020. Advances in Intelligent Systems and Computing, vol 1293. Springer, Cham. https://doi.org/10.1007/978-3-030-63270-0_32

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