METHOD FOR DETERMINING THE MAGNETIC FIELD STRENGTH IN A SHEET OF ELECTRICAL STEEL
DOI:
https://doi.org/10.36910/775.24153966.2025.83.16Keywords:
electrodynamic equations, magnetic field strength, initial value problem, continued fractions, two-sided approximations, electrodynamic equations, magnetic field strength, initial value problem, continued fractions, two-sided approximationsAbstract
This work is devoted to the determination of the periodic component of the magnetic field strength in a layer of electrical
steel. When constructing a mathematical model, the magnetic permeability is approximated by a fractional-rational function.
To calculate the properties of the magnetic field, it is proposed to use two nonlinear methods - the method of the fourth order of
accuracy and the third order of accuracy with a two-sided estimate of the error of the result.
The advantages of this approach are that using only four calculations of the right-hand side of the differential equation,
a method of fourth-order accuracy, two two-sided approximations of third-order accuracy, and an explicit estimate of the main
term of the local error of the result are obtained.
The mathematical model was calculated and analyzed, and the form of the magnetic permeability approximation that
should be used in the study of weak and strong fields was determined.
