| 一种时间分数阶扩散方程初边值问题的隐式有限差分格式 |
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| 引用本文： | 陈春华,卢旋珠.一种时间分数阶扩散方程初边值问题的隐式有限差分格式[J].华东地质学院学报,2006,29(3):289-293. |
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| 作者姓名： | 陈春华 卢旋珠 |
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| 作者单位： | 江苏大学工商管理学院 江苏镇江212013(陈春华)，福州大学数学与计算机学院数学系 福建福州350002(卢旋珠) |
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| 摘 要： | 通过Caputo型与G runwald型的分数阶导数的转化关系以及利用G runwald型的标准数值近似公式对Caputo型分数阶导数进行离散,可构建时间分数阶扩散方程初边值问题的隐式有限差分格式。此差分格式是无条件稳定和无条件收敛的。
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| 关 键 词： | 时间分数阶扩散方程 差分格式 稳定性 收敛性 |
| 文章编号： | 1000-2251(2006)03-289-05 |
| 收稿时间： | 2005-04-26 |
| 修稿时间： | 2005年4月26日 |
A Difference Approximation for Time Fractional Diffusion Equation |
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| CHEN Chun-hua,LU Xuan-zhu.A Difference Approximation for Time Fractional Diffusion Equation[J].Journal of East China Geological Institute,2006,29(3):289-293. |
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| Authors: | CHEN Chun-hua LU Xuan-zhu |
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| Institution: | 1. School of Management, Jiansu University, Zhenjiang, JS 212013, China; 2. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, FJ 350002, China |
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| Abstract: | From the relationship between the Caputo derivative and Grunwald derivative,the discretion for the fractional derivative is proposed by using the standard numerical approximation of Grunwald derivative.Then the difference approximation for the time fractional diffussion equation with initial conditions and boundary conditions is represented.The implicit difference approximation is unconditionally stable and convergent respectively. |
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| Keywords: | the time fractional diffusion equation implicit difference approximation stability convergence |
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