In modeling a wide range of devices containing magnetic cores, it is of a principal significance to provide an adequate description of the transients in the thin sheets or ribbons of conducting ferromagnetic material present in the device. In particular, the important practical problem of magnetization of the wound core is immediately reduced, under the known conditions, to the study of the processes in a separate ribbon. When formulating the boundary value problem (BVP), it should be taken into account that the corresponding numerical scheme is used in a transient simulator, where Maxwell equations are solved together with the ordinary differential equations describing the lumped elements of an electrical circuit. To implement their coupling, the magnetic circuit described by the BVP is considered as a two-pole, across the terminals of which some arbitrary time-variable voltage is applied. This voltage is unknown in advance and should be found in the course of solving the BVP with the Neumann boundary conditions. A comparative analysis of two main approaches to the problem, namely the finite-difference (FD) and finite-element (FE), has been carried out. It is shown that the comparison of their possibilities requires the consideration of nonstandard FD-numerical schemes with the temporal derivative distributed over several neighboring nodes. Two FD-schemes of different accuracy are developed and compared with the corresponding FE-schemes. When solving the linear problem, such schemes are competitive in accuracy with FE-schemes with the same bandwidth of the resulting coefficient matrix. When solving the substantially nonlinear problems, especially the problems that are characterized by abrupt changes in the differential magnetic permeability, the use of high order numerical schemes (both FD and FE) is not justified. One of the best choices for such a case is the second-order central-difference scheme. The method is proposed for incorporation of this scheme in a transient simulator. It is shown that the method developed is sufficiently effective for both the transient evaluation and for the analysis of the steady-state mode that is settled after several cycles of the periodical excitation.

*) The work was supported financially by the GOA-project 99-200/4 and by the research project No 3604209B of FWO-Vlaanderen