| 变系数分数阶反应-扩散方程的数值解法 |
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| 引用本文： | 马亮亮,刘冬兵.变系数分数阶反应-扩散方程的数值解法[J].沈阳大学学报,2014(1):76-80. |
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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（10671132,60673192）;攀枝花学院校级科研项目（2013YB05）. |
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| 摘 要： | 考虑了变系数分数阶反应一扩散方程，将一阶的时间偏导数和二阶的空间偏导数分别用Caputo分数阶导数和Riemann-Liouville分数阶导数替换，利用L1算法和G算法对方程的变系数分数阶导数进行适当的离散，给出了该方程的一种计算有效的隐式差分格式，并证明了这个差分格式是无条件稳定和无条件收敛的，且具有o（τ＋h）收敛阶．最后用数值例子说明差分格式是有效的．
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| 关 键 词： | 变系数 反应一扩散方程 隐式差分 稳定性 收敛性 |
A Numerical Method for Fractional Reaction-Dispersion Equation with Variable Coefficients |
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| Ma Liangliang,Liu Dongbing.A Numerical Method for Fractional Reaction-Dispersion Equation with Variable Coefficients[J].Journal of Shenyang University,2014(1):76-80. |
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| Authors: | Ma Liangliang Liu Dongbing |
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| Institution: | (College of Mathematics and Computer, Panzhihua University, Panzhihua 617000, China) |
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| Abstract: | A fractional reaction-dispersion equation with variable coefficients is considered which the first-order time derivative and the second-order space derivative is replacing by Caputo fractional derivative and Riemann-Liouville derivative respectively, and an implicit difference scheme is presented by using the algorithm of L1 and G to discrete the variable coefficients fractional derivative efficaciously. It is showed that the scheme is unconditional stable and convergence respectively, the convergence order of the scheme is o（τ＋h）. Finally, a numerical example demonstrates the difference method is effective. |
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| Keywords: | variable coefficients reaction-dispersion equation implicit difference stability convergence |
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