| 分数阶扩散-波动方程数值求解 |
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| 引用本文： | 彭文婷,文立平.分数阶扩散-波动方程数值求解[J].福州大学学报(自然科学版),2011,39(4):508-511,516. |
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| 作者姓名： | 彭文婷 文立平 |
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| 作者单位： | 福州大学管理学院;湘潭大学数学与计算科学学院; |
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| 摘 要： | 针对Caputo分数阶导数意义下的时间分数阶扩散-波动方程进行数值研究.利用Caputo分数阶导数与Grunwald-Letnikov分数阶导数的关系对时间分数阶导数进行时间离散化处理,再利用二阶中心差商离散方程中的二阶空间导数,并结合边值条件的离散化,把离散化方程的求解转化为一个线性方程组的求解.利用Matlab编程...
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| 关 键 词： | 扩散-波动方程 分数阶导数 数值解 |
Numerical method for the fractional order diffusion-wave equation |
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| PENG Wen-ting,WEN Li-ping.Numerical method for the fractional order diffusion-wave equation[J].Journal of Fuzhou University(Natural Science Edition),2011,39(4):508-511,516. |
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| Authors: | PENG Wen-ting WEN Li-ping |
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| Institution: | PENG Wen-ting1,WEN Li-ping2(1.College of Management,Fuzhou University,Fuzhou,Fujian 350108,China,2.College of Mathematics and Computer Science,Xiangtan University,Xiangtan,Hunan 411000,China) |
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| Abstract: | Concerned with the numerical solving for the time fractional order diffusion-wave equation defined with the Caputo derivative.First by making use of the relation between the Caputo derivative and the Grunwald-Letnikov derivative,the time fractional derivatives can be discreted.Then the second-order space derivative in the equation is approximated by the second-order central difference quotient.Combined with the discretization of boundary value conditions,the solution of the discretization equations are tran... |
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| Keywords: | diffusion-wave equation fractional order derivative mmerical method |
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