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The model of coupled oscillators plays an important role in modern physics.It is used for description of various processes: from vibrations atoms in solidstates to electromagnetic oscillations in slow-wave structures. The model withshort-range coupling is the most widely used, for which a separate oscillatoris coupled with two adjacent ones only. There are two main types of oscillatorscoupling: capacitive (electric, power) and inductive (magnetic, inertial). Inthe first case, the coupling is proportional to the amplitudes of oscillationsin the adjacent cells, in the second one - to the second derivative of theseamplitudes. For numerical study of dynamics of a system that can be describedby a model of coupled oscillators with an inductive coupling, it is necessaryto find explicit expressions for the second derivatives of the amplitudes. Tofind these expressions, we propose to use the method that is based on thesolution of difference equations. The results of the analysis of this methodare given in the paper.

Analysis of the non-stationary model of coupled oscillators with inductive coupling