| 一个分数阶扩散方程的定解问题的数值解法 |
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| 引用本文： | 池光胜,李功胜,张芳,张涛.一个分数阶扩散方程的定解问题的数值解法[J].四川轻化工学院学报,2013(5):86-89. |
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| 作者姓名： | 池光胜 李功胜 张芳 张涛 |
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| 作者单位： | [1]山东凯文科技职业学院基础教学部,济南250200 [2]山东理工大学理学院应用数学研究所,山东淄博255000 |
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| 基金项目： | 山东凯文科技职业学院自然科学基金项目（KW2012-09） |
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| 摘 要： | 研究了一个扩散系数与空间变量相关的一维空间-时间分数阶扩散方程的定解问题。基于Riemann-Liouville意义下空间导数和Caputo意义下时间导数的离散，提出了一种求解方程的隐式差分格式，验证了这个格式是无条件稳定，并证明了它的收敛性，其收敛的阶为O（τ＋h），最后给出了数值例子。
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| 关 键 词： | 空间-时间分数阶扩散方程 扩散系数与空间变量相关 隐式差分格式 稳定性 收敛性 |
A Numerical Method for the Solution of a Fractional Diffusion Equation |
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| CHI Guang-sheng,LI Gong-sheng,ZHANG Fang,ZHANG Tao.A Numerical Method for the Solution of a Fractional Diffusion Equation[J].Journal of Sichuan Institute of Light Industry and Chemical Technology,2013(5):86-89. |
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| Authors: | CHI Guang-sheng LI Gong-sheng ZHANG Fang ZHANG Tao |
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| Affiliation: | 1. Department of Foundetion Education, Shandong Kaiwen College of Science ＆ Technology, Ji＇nan 250200, China; 2. Institute of Applied Mathematics, Shandong University of Science ＆ Technology, Zibo 255000, China) |
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| Abstract: | The solution of a space-time fractional diffusion equation with spale deperdent diffusion coefficient is studied. An implicit difference scheme is presented based on the dispersion of the space derivatives in sense of Rimmann-Liouville and the time derivatives in sense of Caputo. The format is tested to be unconditional stable and its astringency is proved. The result shows convergence order of the method is O （ τ ＋ h）. Finally, the numerical example is given. |
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| Keywords: | space-time fractional diffusion equation space deperdent diffusion coefficient implicit difference scheme stability convergence |
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