| 带Robin边界条件的分数阶对流-扩散方程的数值解法 |
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| 引用本文： | 曾宝思,尹修草,谢常平,房少梅. 带Robin边界条件的分数阶对流-扩散方程的数值解法[J]. 四川大学学报(自然科学版), 2018, 55(1): 0013-0017 |
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| 作者姓名： | 曾宝思 尹修草 谢常平 房少梅 |
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| 作者单位： | 华南农业大学数学与信息学院数学系,华南农业大学数学与信息学院数学系,华南农业大学数学与信息学院数学系,华南农业大学数学与信息学院数学系 |
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| 基金项目： | 国家自然科学基金（11271141） |
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| 摘 要： | 本文对带Robin边界条件的分数阶对流-扩散方程进行了数值研究.本文利用移位Grünwald公式对Riemann-Liouville空间分数阶导数进行离散,在此基础上建立一种隐式有限差分格式,并讨论了它差分解的存在唯一性,然后分析了该格式的相容性、稳定性和收敛性,最后通过数值算例验证格式是可靠和有效的.
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| 关 键 词： | 分数阶对流-扩散方程；Robin边界；隐式有限差分格式；稳定性；收敛性 |
| 收稿时间： | 2017-10-16 |
| 修稿时间： | 2017-11-22 |
Numerical methods of the fractional advection-dispersion equation with Robin boundary condition |
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| ZENG Bao-Si,YIN Xiu-Cao,XIE Chang-Ping and FANG Shao-Mei. Numerical methods of the fractional advection-dispersion equation with Robin boundary condition[J]. Journal of Sichuan University (Natural Science Edition), 2018, 55(1): 0013-0017 |
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| Authors: | ZENG Bao-Si YIN Xiu-Cao XIE Chang-Ping FANG Shao-Mei |
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| Affiliation: | Department of mathematics and information, south China agricultural university,Department of mathematics and information, south China agricultural university,Department of mathematics and information, south China agricultural university |
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| Abstract: | In this paper, we study the practical numerical methods to solve the fractional advection-dispersion equation with Robin boundary condition. We propose an implicit finite difference scheme based on the shifted Grünwald formula to discretize Riemann-Liouville fractional derivative. Existence and uniqueness of numerical solutions are derived. It is proved that the implicit finite difference scheme is unconditionally stable and convergent. Finally, numerical simulations show that the method is efficient. |
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| Keywords: | Fractional advection-dispersion equation Robin boundary Implicit finite difference method Unconditionally stability Convergence |
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