School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
School of Science, Xi’an Polytechnic University, Xi’an 710048, China
: Received: 30 August 2016 / Approved: 30 August 2016 / Online: 30 August 2016 (12:29:12 CEST)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
How to cite:
Yan, T.; Luo, S. Local Polynomial Smoother for Solving Bagley-Torvik Fractional Differential Equations. Preprints2016, 2016080231 (doi: 10.20944/preprints201608.0231.v1).
Yan, T.; Luo, S. Local Polynomial Smoother for Solving Bagley-Torvik Fractional Differential Equations. Preprints 2016, 2016080231 (doi: 10.20944/preprints201608.0231.v1).
Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.
numerical solution; Bagley-Torvik fractional differential equations; local polynomial smoother