| NUMERICAL SOLUTION OF THE SPACE FRACTIONAL DIFFERENTIAL EQUATION |
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| 引用本文： | Zheng Dayi Lu Xuanzhu (College of Math,and Computer Science,Fuzhou University,Fuzhou 350002) Liu Fawang (School of Math. Sciences,Xiamen University,Xiamen 361005). NUMERICAL SOLUTION OF THE SPACE FRACTIONAL DIFFERENTIAL EQUATION[J]. Annals of Differential Equations, 2005, 21(3): 518-524 |
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| 作者姓名： | Zheng Dayi Lu Xuanzhu (College of Math and Computer Science Fuzhou University Fuzhou 350002) Liu Fawang (School of Math. Sciences Xiamen University Xiamen 361005) |
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| 作者单位： | Zheng Dayi Lu Xuanzhu (College of Math，and Computer Science，Fuzhou University，Fuzhou 350002) Liu Fawang (School of Math. Sciences，Xiamen University，Xiamen 361005) |
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| 摘 要： | In this paper, a space fractional differential equation is considered. The equation is obtained from the parabolic equation containing advection, diffusion and reaction terms by replacing the second order derivative in space by a fractional derivative in space of order. An implicit finite difference approximation for this equation is presented. The stability and convergence of the finite difference approximation are proved. A fractional-order method of lines is also presented. Finally, some numerical results are given.
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| 关 键 词： | 空间分数微分方程 数字解 有限积分 稳定性 收敛性 |
NUMERICAL SOLUTION OF THE SPACE FRACTIONAL DIFFERENTIAL EQUATION |
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| Zheng Dayi Lu Xuanzhu Liu Fawang. NUMERICAL SOLUTION OF THE SPACE FRACTIONAL DIFFERENTIAL EQUATION[J]. 微分方程年刊(英文版), 2005, 21(3): 518-524 |
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| Authors: | Zheng Dayi Lu Xuanzhu Liu Fawang |
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| Affiliation: | [1]College of Math. and Computer Science, Fuzhou University, Fuzhou 350002 [2]School of Math. Sciences, Xiamen University, Xiamen 361005 |
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| Abstract: | In this paper, a space fractional differential equation is considered. The equation is obtained from the parabolic equation containing advection, diffusion and reaction terms by replacing the second order derivative in space by a fractional derivative in space of order. An implicit finite difference approximation for this equation is presented. The stability and convergence of the finite difference approximation are proved. A fractional-order method of lines is also presented. Finally, some numerical results are given. |
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| Keywords: | space fractional differential equation implicit finite difference approximation stability convergence |
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