| 空间-时间分数阶对流扩散方程的数值解法 |
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| 引用本文： | 覃平阳,张晓丹.空间-时间分数阶对流扩散方程的数值解法[J].计算数学,2008,30(3):305-310. |
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| 作者姓名： | 覃平阳 张晓丹 |
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| 作者单位： | 北京科技大学应用科学学院数力系,北京,100083 |
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| 摘 要： | 本文考虑一个空间-时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时间一阶导数用α(0＜α＜1)阶导数代替,空间二阶导数用β(1＜β＜2)阶导数代替.本文提出了一个隐式差分格式,验证了这个格式是无条件稳定的,并证明了它的收敛性,其收敛阶为O(ι 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 隐式差分格式 稳定性 收敛性 |
A NUMERICAL METHOD FOR THE SPACE-TIME FRACTIONAL CONVECTION-DIFFUSION EQUATION |
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| Qin Pingyang,Zhang Xiaodan.A NUMERICAL METHOD FOR THE SPACE-TIME FRACTIONAL CONVECTION-DIFFUSION EQUATION[J].Mathematica Numerica Sinica,2008,30(3):305-310. |
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| Authors: | Qin Pingyang Zhang Xiaodan |
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| Institution: | Department of Mathematics and Mechanics, Applied Science School, University of Science and Technology Beijing, Beijing 100083, China |
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| Abstract: | In this paper, a space-time fractional convection-diffusion equation is considered. The equation is obtained from the classical convection-diffusion equation by replacing the first-order time derivative, the second-order space derivative with fractional derivatives of order $\alpha$($0<\alpha<1$), $\beta$ ($1<\beta<2$)respectively. An implicit difference scheme is presented. It is shown that the method is unconditional stable and the convergence order of the method is $O(\tau+h)$ . Finally, some numerical examples are given. |
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| Keywords: | convection-diffusion equation fractional-order derivative implicit difference scheme stability convergence |
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