Geodesic
Mathematical modelling of hereditarity Airy oscillator with friction
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 1, pp. 138-148

Voir la notice de l'article provenant de la source Math-Net.Ru

Work is devoted to mathematical modelling hereditarity oscillatory systems with the help of the mathematical apparatus of fractional calculus on the example of an Airy oscillator with friction. Model Airy equation was written in terms of Gerasimov–Caputo fractional derivatives. Next a finite-difference scheme to this generalized equation for numerical computation was proposed. The problems of approximation, stability and convergence of a numerical scheme are considered. The results of simulations are presented based on numerical solutions waveforms and phase trajectories depending on different values of the control parameters are built.
Keywords: Airy oscillator; hereditarity; Gerasimov–Caputo derivative; finite-difference scheme; the phase trajectory. 
@article{VYURU_2017_10_1_a8,
     author = {R. I. Parovik},
     title = {Mathematical modelling of hereditarity {Airy} oscillator with friction},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {138--148},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_1_a8/}
}
TY  - JOUR
AU  - R. I. Parovik
TI  - Mathematical modelling of hereditarity Airy oscillator with friction
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2017
SP  - 138
EP  - 148
VL  - 10
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VYURU_2017_10_1_a8/
LA  - ru
ID  - VYURU_2017_10_1_a8
ER  - 
%0 Journal Article
%A R. I. Parovik
%T Mathematical modelling of hereditarity Airy oscillator with friction
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2017
%P 138-148
%V 10
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VYURU_2017_10_1_a8/
%G ru
%F VYURU_2017_10_1_a8
R. I. Parovik. Mathematical modelling of hereditarity Airy oscillator with friction. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 1, pp. 138-148. http://geodesic.mathdoc.fr/item/VYURU_2017_10_1_a8/