Mathematical Models of Oscillators with Memory

Roman Ivanovich Parovik

A chapter in Oscillators - Recent Developments from IntechOpen

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.

Keywords: mathematical model; cauchy problem; heredity; derivative of fractional order; finite-difference scheme; stability; convergence; oscillograms; phase trajectory (search for similar items in EconPapers)
JEL-codes: C60 (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:169296

DOI: 10.5772/intechopen.81858

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