Solving Highly-dimensional Fractional Oscillators via an Efficient Scheme Based on Adams and Newmark-β Algorithms

DOI

10.2991/eame-18.2018.69How to use a DOI?

Keywords

fractional derivative; nonlinear oscillator; volterra integral equation; newmark-β method; adams scheme

Abstract

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.

Copyright

© 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/).

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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  -