Численный анализ математических моделей дробных осцилляторов

In this paper, a class of fractional oscillators is proposed, which are described using an integro-differential equation with difference kernels – memory functions. The memoryfunctions were selected by power, which made it possible to switch to fractional-order derivatives in the initial model equation. Further, using approximations of fractional derivatives, a non-local explicit finite-difference scheme was constructed with the first order of approximation to find a numerical solution of a model equation with fractionalorder derivatives. Using test examples, taking into account the Runge rule, the computational accuracy of the numerical algorithm was calculated. It is shown that as the discretization step of the calculated regular grid decreases, the maximum error also decreases by half, and the computational accuracy tends to unity, which corresponds to the order of approximation of the circuit. Using the developed numerical algorithm, oscillograms and phase trajectories of various fractional oscillators were constructed and investigated. It is shown that the numerical algorithm gives adequate results and can be used in the simulation of oscillatory processes with memory.used in the simulation of oscillatory processes with memory.

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