| 一类分数阶对流扩散方程差分格式的理论分析 |
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| 引用本文： | 马亮亮,刘冬兵.一类分数阶对流扩散方程差分格式的理论分析[J].五邑大学学报(自然科学版),2014(2):9-14. |
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| 作者姓名： | 马亮亮 刘冬兵 |
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| 作者单位： | 攀枝花学院数学与计算机学院,四川攀枝花617000 |
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| 基金项目： | 国家自然科学基金资助项目（No.10671132.No.60673192））;四川省科技厅资助项目（2013JY0125）;攀枝花学院校级培育项目（2012PY08）;攀枝花学院校级科研项目（2013YB05）;攀枝花学院院级科研创新项目（Y2013.04）. |
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| 摘 要： | 考虑一般的对流扩散方程,将一阶的时间导数用Caputo分数阶导数替换,二阶的空间导数用Riemann-Liouville分数阶导数替换,得到了一个Riemann-Liouville-Caputo分数阶对流扩散方程.给出了这个方程的一种计算有效的隐式差分格式,并证明了该差分格式是无条件稳定、无条件收敛的,其收敛阶为O(l+h).最后给出了数值例子.
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| 关 键 词： | 对流扩散方程 Caputo导数 Riemann-Liouville导数 隐式差分格式 |
A Difference Scheme and a Theorem Analysis for a Kind of Fractional Convection-Dispersion Equation |
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| MA Liang-liang,LIU Dong-bing.A Difference Scheme and a Theorem Analysis for a Kind of Fractional Convection-Dispersion Equation[J].Journal of Wuyi University(Natural Science Edition),2014(2):9-14. |
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| Authors: | MA Liang-liang LIU Dong-bing |
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| Institution: | (College of Mathematics and Computer Science, Panzhihua University, Panzhihua 617000, China) |
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| Abstract: | A classical convection-dispersion equation in which the first-order time derivative was replaced by a Caputo derivative and the second-order space derivative was replaced by a Riemann-Liouville derivative was considered, and a Riemann-Liouville-Caputo fractional convection-dispersion equation was obtained. A computationally effective implicit difference approximation was presented. It was shown that the scheme was unconditionally stable and convergent respectively. The convergence order of the scheme was （ ）Oτ＋h . Finally, some numerical examples were given. |
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| Keywords: | convection-dispersion equations Caputo derivatives Riemann-Liouville derivatives implicit difference schemes |
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