| 一类变时间分数阶含源项非定常奇异摄动对流扩散方程的数值分析 |
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| 引用本文： | 马亮亮,刘冬兵.一类变时间分数阶含源项非定常奇异摄动对流扩散方程的数值分析[J].沈阳大学学报,2013(5):424-427. |
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| 作者姓名： | 马亮亮 刘冬兵 |
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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（10671132,60673192）;四川省科技厅资助项目（2012PY08）. |
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| 摘 要： | 考虑了变时间分数阶含源项非定常奇异摄动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： | 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 for Non-Constant Singularly with Source Term a Class of Variable Order Time Fractional Perturbed Convection Diffusion Equation |
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| Ma Liangliang,Liu Dongbing.Numerical Analysis for Non-Constant Singularly with Source Term a Class of Variable Order Time Fractional Perturbed Convection Diffusion Equation[J].Journal of Shenyang University,2013(5):424-427. |
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| Authors: | Ma Liangliang Liu Dongbing |
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| Institution: | (College of Mathematics and Computer, Panzhihua University, Panzhihua 617000, China) |
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| Abstract: | A class of variable order time fractional non-constant singularly perturbed convection diffusion equation with source term is considered. Firstly, numerical approximation scheme has been proposed by using the method of the piecewise linear interpolation join with a second order approximation of the first order time derivative to discrete the Coimbra variable order time fractional derivative. Then, 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: | convection diffusion equation Coimbra variable order fractional derivative numerical approximation central difference spatial fractional derivative |
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