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Mathematical Models of Oscillators with Memory

In: Oscillators - Recent Developments

Author

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  • Roman Ivanovich Parovik

Abstract

The chapter proposes a mathematical model for a wide class of hereditary oscillators, which is a Cauchy problem in the local formulation. As an initial model equation, an integrodifferential equation of Voltaire type was introduced, which was reduced by means of a special choice of difference kernels to a differential equation with nonlocal derivatives of fractional-order variables. An explicit finite-difference scheme is proposed, and questions of its stability and convergence are investigated. A computer study of the proposed numerical algorithm on various test examples of the hereditary oscillators Airy, Duffing, and others was carried out. Oscillograms and phase trajectories are plotted and constructed.

Suggested Citation

  • Roman Ivanovich Parovik, 2019. "Mathematical Models of Oscillators with Memory," Chapters, in: Patrice Salzenstein (ed.), Oscillators - Recent Developments, IntechOpen.
    • Handle: RePEc:ito:pchaps:169296
    DOI: 10.5772/intechopen.81858
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    More about this item

    Keywords

    mathematical model; cauchy problem; heredity; derivative of fractional order; finite-difference scheme; stability; convergence; oscillograms; phase trajectory;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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