Proceedings of the 2019 International Conference on Modeling, Analysis, Simulation Technologies and Applications (MASTA 2019)

A Fast Method for Solving the Bagley-Torvik Equation with Time Delay as Delay Differential Equations of Integer Order

Authors
Yong Xu, Qi-xian Liu, Ji-ke Liu
Corresponding Author
Qi-xian Liu
Available Online July 2019.
DOI
https://doi.org/10.2991/masta-19.2019.32How to use a DOI?
Keywords
Time delay, Bagley-Torvik equation, Separation of variables, Hopf bifurcation
Abstract

A method of solving the Bagley-Torvik equation with time delay has been presented in this article, which is based on the physical meaning of that equation and thus avoid the history dependence of it. The most important thing is that the fractional term of the Bagley-Torvik equation is transformed into a solution of a partial differential equation, which is then converted into a set of ordinary differential equations afterwards. An approximation of a boundary condition of the partial differential equations is used as a crucial point. Numerical results have indicated that the computational efficiency has improved significantly. We consider a numerical example with Hopf bifurcation caused by time delay of the Bagley-Torvik equation, which shows that the presented method is computationally more efficient than the predictor-corrector (PC) algorithm with the same time step length.

Copyright
© 2019, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2019 International Conference on Modeling, Analysis, Simulation Technologies and Applications (MASTA 2019)
Series
Advances in Intelligent Systems Research
Publication Date
July 2019
ISBN
978-94-6252-761-4
ISSN
1951-6851
DOI
https://doi.org/10.2991/masta-19.2019.32How to use a DOI?
Copyright
© 2019, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Yong Xu
AU  - Qi-xian Liu
AU  - Ji-ke Liu
PY  - 2019/07
DA  - 2019/07
TI  - A Fast Method for Solving the Bagley-Torvik Equation with Time Delay as Delay Differential Equations of Integer Order
BT  - Proceedings of the 2019 International Conference on Modeling, Analysis, Simulation Technologies and Applications (MASTA 2019)
PB  - Atlantis Press
SP  - 186
EP  - 193
SN  - 1951-6851
UR  - https://doi.org/10.2991/masta-19.2019.32
DO  - https://doi.org/10.2991/masta-19.2019.32
ID  - Xu2019/07
ER  -