| 变系数空间分数阶对流-扩散方程的有限差分解法 |
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| 引用本文： | 马亮亮.变系数空间分数阶对流-扩散方程的有限差分解法[J].沈阳大学学报,2013,25(4):341-344. |
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| 作者姓名： | 马亮亮 |
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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，四川省科技厅资助项目 |
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| 摘 要： | 考虑了一个变系数空间分数阶对流-扩散方程.这个方程是将一般的对流-扩散方程中的空间二阶导数用β(1<β≤2)阶导数代替.提出了一个隐式差分格式,验证了这个差分格式是无条件稳定的,并证明了它的收敛性,其收敛阶为o(τ+h),最后给出了数值例子.
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| 关 键 词： | 对流-扩散方程 分数阶导数 隐式差分 稳定性 收敛性 |
Finite Difference Methods for Space Fractional Convection-diffusion Equation with Variable Coefficients |
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| Ma Liangliang.Finite Difference Methods for Space Fractional Convection-diffusion Equation with Variable Coefficients[J].Journal of Shenyang University,2013,25(4):341-344. |
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| Authors: | Ma Liangliang |
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| Institution: | Ma Liangliang (College of Mathematics and Computer, Panzhihua University, Panzhihua 617000, China) |
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| Abstract: | A space fractional convection-diffusion equation is considered. The equation is obtained from the classical convection-diffusion equation by replacing the second-order space derivative with fractional derivative of orderβ（1〈β≤2）. An implicit difference scheme is presented. It is shown that the method is unconditional stable and the convergence order of the method is o（r＋h）. Finally, some numerical examoles are given. |
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| Keywords: | convection-diffusion equation fractional-order derivative implicit difference stability convergence |
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