| 变时间分数阶非定常对流扩散方程的数值分析 |
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| 引用本文： | 马亮亮.变时间分数阶非定常对流扩散方程的数值分析[J].丹东纺专学报,2013(3):207-210. |
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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（60673192）;攀枝花学院校级培育项目（2012PY08）;攀枝花学院院级科研创新项目（2013-04） |
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| 摘 要： | 考虑变时间分数阶非定常对流扩散方程的数值逼近问题,首先,采用分段线性插值法结合对一阶时间导数的一个二阶近似离散Coimbra变时间分数阶导数,然后,用中心差分离散一阶空间分数阶导数和二阶空间分数阶导数。最后,用数值例子验证了提出的数值方法,说明了数值方法的有效性。
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| 关 键 词： | 变时间分数阶对流扩散方程 Coimbra变分数阶导数 数值逼近 中心差分 空间分数阶导数 |
Numerical Analysis of Variable Order Time Fractional Unsteady Convection Diffusion Equation |
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| MA Liang-liang.Numerical Analysis of Variable Order Time Fractional Unsteady Convection Diffusion Equation[J].Journal of Dandong Textile College,2013(3):207-210. |
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| Authors: | MA Liang-liang |
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| Affiliation: | MA Liang-liang(College of Mathematics and Computer,Panzhihua University,Panzhihua 617000,China) |
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| Abstract: | The variable order time fractional unsteady convection diffusion equation was studied.Numerical approximation scheme has been proposed by using the method of the piecewise linear interpolation combined with a second order approximation of the first order time derivative to discrete the Coimbra variable order time fractional derivative.Furthermore,central difference is used to approximate the first order and second order of the spatial fractional derivatives.Finally,a numerical example has been presented to verify the numerical technique,which shows the efficiency of the numerical method. |
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| Keywords: | variable order time fractional convection diffusion equation Coimbra variable order fractional derivative numerical approximation central difference spatial fractional derivative |
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