| 分数阶电报方程的Chebyshev多项式数值解法研究 |
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| 引用本文： | 牛变玲,李灯熬,赵富强,解加全.分数阶电报方程的Chebyshev多项式数值解法研究[J].工程数学学报,2018,35(1):79-87. |
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| 作者姓名： | 牛变玲 李灯熬 赵富强 解加全 |
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| 作者单位： | 1- 太原理工大学信息化管理与建设中心，太原0300242- 太原理工大学信息工程学院，太原0300243- 太原科技大学机械工程学院，太原030024 |
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| 基金项目： | 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). |
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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．
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| 关 键 词： | Chebyshev多项式 分数阶电报方程 数值解 Tau方法 |
| 收稿时间： | 2016-10-12 |
Research of Numerical Methods for Solving Fractional-order Telegraph Equations Based on Chebyshev Polynomials |
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| NIU Bian-ling,LI Deng-ao,ZHAO Fu-qiang,XIE Jia-quan.Research of Numerical Methods for Solving Fractional-order Telegraph Equations Based on Chebyshev Polynomials[J].Chinese Journal of Engineering Mathematics,2018,35(1):79-87. |
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| Authors: | NIU Bian-ling LI Deng-ao ZHAO Fu-qiang XIE Jia-quan |
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| Affiliation: | 1- Institution of Information Management and Development, Taiyuan University of Technology, Taiyuan 030024
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2- College of Information Engineering, Taiyuan University of Technology, Taiyuan 030024
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3- College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024 |
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| 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. |
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| Keywords: | Chebyshev polynomials fractional-order telegraph equations numerical solutions Tau method |
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