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

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.