Solving Highly-dimensional Fractional Oscillators via an Efficient Scheme Based on Adams and Newmark-β Algorithms
- 10.2991/eame-18.2018.69How to use a DOI?
- fractional derivative; nonlinear oscillator; volterra integral equation; newmark-β method; adams scheme
In this paper, we employed an efficient numerical scheme by combining Adams and Newmark-β algorithms to solve highly-dimensional nonlinear oscillators containing fractional derivatives (FDs). The method solves the original equations directly by incorporating the Adams and Newmark-β algorithms to handle FDs and integer derivatives, respectively. It also provides a strategy to avoid nonlinear algebraic equations arising in the Newmark-β algorithm. Both analytical estimations and numerical results show that the presented method is second-order accurate. The applicability and efficiency of the presented method are demonstrated by a simple and feasible extension to solve time fractional nonlinear diffusion-wave equations.
- © 2018, 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 - Yuxiang Chen AU - Yanmao Chen AU - Qixian Liu PY - 2018/06 DA - 2018/06 TI - Solving Highly-dimensional Fractional Oscillators via an Efficient Scheme Based on Adams and Newmark-β Algorithms BT - Proceedings of the 2018 3rd International Conference on Electrical, Automation and Mechanical Engineering (EAME 2018) PB - Atlantis Press SP - 325 EP - 329 SN - 2352-5401 UR - https://doi.org/10.2991/eame-18.2018.69 DO - 10.2991/eame-18.2018.69 ID - Chen2018/06 ER -