| 带非线性源项的双侧空间分数阶扩散方程的隐式中点方法 |
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| 引用本文： | 胡冬冬,曹学年,蒋慧灵. 带非线性源项的双侧空间分数阶扩散方程的隐式中点方法[J]. 计算数学, 2019, 41(3): 295-307. DOI: 10.12286/jssx.2019.3.295 |
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| 作者姓名： | 胡冬冬 曹学年 蒋慧灵 |
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| 作者单位： | 湘潭大学数学与计算科学学院, 湘潭 411105 |
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| 摘 要： | 本文用隐式中点方法离散一阶时间偏导数，并用拟紧差分算子逼近Riemann-Liouville空间分数阶偏导数，构造了求解带非线性源项的空间分数阶扩散方程的数值格式.给出了数值方法的稳定性和收敛性分析.数值试验表明数值方法是有效的.
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| 关 键 词： | 双侧空间分数阶扩散方程 隐式中点方法 拟紧差分算子 稳定性 收敛性 |
| 收稿时间： | 2017-12-14 |
THE IMPLICIT MIDPOINT METHOD FOR TWO-SIDE SPACE FRACTIONAL DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM |
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| Hu Dongdong,Cao Xuenian,Jiang Huiling. THE IMPLICIT MIDPOINT METHOD FOR TWO-SIDE SPACE FRACTIONAL DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM[J]. Mathematica Numerica Sinica, 2019, 41(3): 295-307. DOI: 10.12286/jssx.2019.3.295 |
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| Authors: | Hu Dongdong Cao Xuenian Jiang Huiling |
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| Affiliation: | School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China |
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| Abstract: | In this paper, the numerical scheme was constructed for solving the space fractional diffusion equation with a nonlinear source term where the implicit midpoint method was applied to discretize the first order time partial derivative, and the quasi-compact difference operator was utilized to approximate Riemann-Liouville space fractional partial derivative. Stability and convergence analysis of this numerical method were given. Numerical experiments show that the numerical method is effective. |
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| Keywords: | Two-side space fractional diffusion equation Implicit midpoint method Quasi-compact difference operator Stability Convergence |
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