A Fast Method for Solving the Bagley-Torvik Equation with Time Delay as Delay Differential Equations of Integer Order
- DOI
- 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/).
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 - 10.2991/masta-19.2019.32 ID - Xu2019/07 ER -