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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (1): 88-100.doi: 10.3969/j.issn.1005-3085.2018.01.009

• • 上一篇    下一篇

数值求解Bagley-Torvik分数阶微分方程的局部多项式光滑因子方法（英）

罗双华1,   王   松1,   张成毅1,   刘庆兵2   

  1. 1- 西安工程大学理学院，西安  710048
    2- 浙江万里学院理学院，宁波  315100
  • 收稿日期:2015-11-11 接受日期:2017-06-28 出版日期:2018-02-15 发布日期:2018-04-15
  • 基金资助:
    国家自然科学基金(11601409)；陕西省自然科学基金(2016JM1009)；陕西省教育厅科学基金(17JK0344)；浙江省国家自然科学基金(LY14A010007;LQ14G010002)；宁波市自然科学基金(2015A610173).

Local Polynomial Smoother for Solving Bagley-Torvik Fractional Differential Equations

LUO Shuang-hua1,   WANG Song1,   ZHANG Cheng-yi1,   LIU Qing-bing2   

  1. 1- School of Science, Xi'an Polytechnic University, Xi'an 710048
    2- School of Science, Zhejiang Wanli University, Ningbo 315100
  • Received:2015-11-11 Accepted:2017-06-28 Online:2018-02-15 Published:2018-04-15
  • Supported by:
    The National Natural Science Foundations of China (11601409); the Natural Science Foundation of Shaanxi Province (2016JM1009); the Science Foundation of the Education Department of Shaanxi Province (17JK0344); the National Natural Science Foundation of Zhejiang Province (LY14A010007; LQ14G010002); the Natural Science Foundation of Ningbo (2015A610173).

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摘要： 为了得到Bagley-Torvik分数阶微分方程的数值解，我们提出了局部多项式光滑因子（LPS）方法．首先，我们构建了LPS方法，重点强调了该方法的主要思想．然后，用该方法数值求解Bagley-Torvik分数阶微分方程．数值实验表明：该方法比Legendre运算矩阵方法和伪谱方法更加有效更加精确．

关键词: 数值解, 局部多项式光滑因子（LPS）方法, Bagley-Torvik分数微分方程

Abstract: The local polynomial smoother (LPS) method is proposed in this paper to derive the numerical solution of the Bagley-Torvik fractional-order differential equations. Firstly, the local polynomial smoother method is well constructed and its main thinking is emphasized. Then this method is employed to solve the Bagley-Torvik FDEs. Finally, some numerical comparison experiments with some other methods are made to demonstrate that the LPS method proposed is more efficient and more accurate than Legendre operational matrix method and pseudo-spectral method.

Key words: numerical solution, local polynomial smoother (LPS) method, Bagley-Torvik fractional differential equations

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