When solving the boundary integral equation with respect to the density of a double layer of fictitious magnetic charges in the case of using a piecewise constant approximation of double layer density, the interface conditions for the field vectors are not fulfilled at any point of the interface between ferromagnetic media. The article shows that these interface conditions are satisfied not discretely but integrally. Based on the proposed integral relations, which are derived from the Ampere's

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... ircuital Law, a new system of linear equations is derived. The system of linear equations is obtained with respect to the piecewise constant approximation coefficients of double layer magnetic charge density. The resulting system of equations does not contain the scalar magnetic potential of free sources. Consequently, this numerical model can be directly applied to the analysis of magnetic field in any multiply connected domains without introducing impenetrable partitions or solving an additional boundary value problem for finding scalar magnetic potential.