| 时间分数阶扩散方程的隐式差分近似 |
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| 引用本文： | 马亮亮. 时间分数阶扩散方程的隐式差分近似[J]. 贵州师范大学学报(自然科学版), 2014, 0(2): 79-82 |
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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（No.60673192）;攀枝花学院校级培育项目（No.2012PY08） |
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| 摘 要： | 考虑时间分数阶扩散方程,它是从标准的扩散方程中用分数阶导数α(0α1)代替一阶时间导数而得到,提出了一个计算有效的隐式差分近似,并证明了这个隐式差分近似是无条件稳定和无条件收敛的。最后给出了数值例子。
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| 关 键 词： | 时间分数阶 扩散方程 隐式差分近似 稳定性 收敛性 |
Implicit difference approximation for the time fractional order diffusion equation |
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| MA Liangliang. Implicit difference approximation for the time fractional order diffusion equation[J]. Journal of Guizhou Normal University(Natural Sciences), 2014, 0(2): 79-82 |
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| Authors: | MA Liangliang |
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| Affiliation: | MA Liangliang(College of Mathematics and Computer, Panzhihua University, Panzhihua, Sichuan 617000, China) |
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| Abstract: | Time fractional order diffusion equation was considered,which obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivation of order α（0 ＜α ＜ 1）.A computationally effective implicit difference approximation was proposed,and the fractional implicit difference approximation was proved unconditional stable and unconditional convergence.Finally,some numerical examples were given. |
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| Keywords: | time fractional order diffusion equation implicit difference approximation stability convergence |
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