## 留言板

 引用本文: 陈虹伶，李小林. 分数阶Cable方程的有限点法分析 [J]. 应用数学和力学，2022，43（6）：700-706
CHEN Hongling, LI Xiaolin. Analysis of the Finite Point Method for Fractional Cable Equations[J]. Applied Mathematics and Mechanics, 2022, 43(6): 700-706. doi: 10.21656/1000-0887.420183
 Citation: CHEN Hongling, LI Xiaolin. Analysis of the Finite Point Method for Fractional Cable Equations[J]. Applied Mathematics and Mechanics, 2022, 43(6): 700-706.

## 分数阶Cable方程的有限点法分析

##### doi: 10.21656/1000-0887.420183

###### 作者简介:陈虹伶（1996—），女，硕士 ( E-mail：913626174@qq.com)李小林（1983—），男，教授, 博士 (通讯作者. E-mail：lxlmath@163.com)
• 中图分类号: O241.82

## Analysis of the Finite Point Method for Fractional Cable Equations

• 摘要:

通过采用中心差分格式离散Riemann-Liouville时间分数阶导数和用有限点法建立离散代数系统，提出了数值求解分数阶Cable方程的无网格有限点法，详细推导了该方法的理论误差估计。数值算例证实了该方法的有效性和收敛性，并验证了理论分析结果。

• 图  1  算例在$\alpha = 0.2 $$\beta = 0.8$$ T = 5 $$h = {1 /{20}}$$ \tau = 1/20$时的数值解和误差：(a) 数值解；(b) 误差

Figure  1.  Numerical solution results and errors gained with $\alpha = 0.2$, $\beta = 0.8$, $T = 5 $$h = 1/20 and \tau = 1/20 : (a) numerical solution results; (b) errors 图 2 h=0.01，T=1时误差与时间步长 \tau 的关系：(a) 相对误差；(b) {L^\infty } 误差 Figure 2. The relationship between relative errors and {L^\infty } errors obtained for h=0.01 and T=1 with respect to time-step size \tau : (a) relative errors ; (b) {L^\infty } errors 图 3 \tau = 0.000\;1,\;T=1时误差与节点间距 h 的关系：(a) 相对误差；(b) {L^\infty } 误差 Figure 3. The relationship between relative errors and {L^\infty } errors obtained for \tau = 0.000\;1\; {\rm{and}} \;\;T=1 with respect to nodal spacing h : (a) relative errors ; (b) {L^\infty } errors 图 4 算例在 \gamma = 0.4$$ T = 5 $$h = {1 / {20}}$$ \tau = 1/20$时的数值解和误差：(a) 数值解；(b) 误差

Figure  4.  Numerical solution results and errors gained with $\gamma = 0.4$, $T = 5$, $h = 1/20$ and $\tau = 1/20$: (a) numerical solution results; (b) errors

图  5  误差与时间步长$\tau$和节点间距$h$的关系：(a) 时间步长$\tau$；(b) 节点间距$h$

Figure  5.  The relationship between the errors and time-step size $\tau$ as well as nodal spacing $h$: (a) for time-step size $\tau$; (b) for nodal spacing $h$

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##### 出版历程
• 收稿日期:  2021-07-02
• 修回日期:  2021-09-19
• 网络出版日期:  2022-06-02
• 刊出日期:  2022-06-30

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