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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): 79-87.doi: 10.3969/j.issn.1005-3085.2018.01.008

• • 上一篇    下一篇

分数阶电报方程的Chebyshev多项式数值解法研究

牛变玲1,   李灯熬2,   赵富强3,   解加全3   

  1. 1- 太原理工大学信息化管理与建设中心，太原  030024
    2- 太原理工大学信息工程学院，太原  030024
    3- 太原科技大学机械工程学院，太原  030024
  • 收稿日期:2016-10-12 接受日期:2017-04-30 出版日期:2018-02-15 发布日期:2018-04-15
  • 通讯作者: 李灯熬 E-mail: lidengao@tyut.edu.cn
  • 基金资助:
    国家自然科学基金(61371062)；太原科技大学博士后科研基金(20152034)；太原科技大学博士启动基金(20122054).

Research of Numerical Methods for Solving Fractional-order Telegraph Equations Based on Chebyshev Polynomials

NIU Bian-ling1,  LI Deng-ao2,  ZHAO Fu-qiang3,  XIE Jia-quan3   

  1. 1- Institution of Information Management and Development, Taiyuan University of Technology, Taiyuan 030024
    2- College of Information Engineering, Taiyuan University of Technology, Taiyuan 030024
    3- College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024
  • Received:2016-10-12 Accepted:2017-04-30 Online:2018-02-15 Published:2018-04-15
  • Contact: D. Li. E-mail address: lidengao@tyut.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (61371062); the Postdoctoral Research Foundation of Taiyuan University of Science and Technology (20152034); the Doctor Startup Foundation of Taiyuan University of Science and Technology (20122054).

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摘要： 分数阶电报方程作为通信工程中的一类重要方程，在实际应用中往往很难求得解析解，因而对其进行数值求解就显得至关重要．为了求得分数阶电报方程的数值解，本文借助Chebyshev多项式函数构造相应的微分算子矩阵，并结合Tau方法将待求方程转化为非线性代数方程组，然后对该方程组进行数值离散求解，最后给出的数值算例也验证了该方法的可行性及有效性．

关键词: Chebyshev多项式, 分数阶电报方程, 数值解, Tau方法

Abstract: Fractional-order telegraph equation is regarded as one of most important equations in communication engineering, which is hard to obtain the analytical solution, so it is crucial to study the numerical methods. In order to obtain the numerical solutions of fractional-order telegraph equations, this study derives the corresponding differential operational matrix through Chebyshev polynomials. Furthermore, the nonlinear telegraph equation is transformed into the system of algebra equations with known coefficients. Then, the numerical solutions can be obtained by solving the system. Lastly, the numerical example is proposed to verify the feasibility and effectiveness.

Key words: Chebyshev polynomials, fractional-order telegraph equations, numerical solutions, Tau method

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