Version 1
: Received: 30 August 2016 / Approved: 30 August 2016 / Online: 30 August 2016 (12:29:12 CEST)
How to cite:
Yan, T.; Luo, S. Local Polynomial Smoother for Solving Bagley-Torvik Fractional Differential Equations. Preprints2016, 2016080231. https://doi.org/10.20944/preprints201608.0231.v1
Yan, T.; Luo, S. Local Polynomial Smoother for Solving Bagley-Torvik Fractional Differential Equations. Preprints 2016, 2016080231. https://doi.org/10.20944/preprints201608.0231.v1
Yan, T.; Luo, S. Local Polynomial Smoother for Solving Bagley-Torvik Fractional Differential Equations. Preprints2016, 2016080231. https://doi.org/10.20944/preprints201608.0231.v1
APA Style
Yan, T., & Luo, S. (2016). Local Polynomial Smoother for Solving Bagley-Torvik Fractional Differential Equations. Preprints. https://doi.org/10.20944/preprints201608.0231.v1
Chicago/Turabian Style
Yan, T. and Shuanghua Luo. 2016 "Local Polynomial Smoother for Solving Bagley-Torvik Fractional Differential Equations" Preprints. https://doi.org/10.20944/preprints201608.0231.v1
Abstract
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.
Keywords
numerical solution; Bagley-Torvik fractional differential equations; local polynomial smoother
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright:
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.