计算数学
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计算数学  2019, Vol. 41 Issue (3): 295-307    DOI:
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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
胡冬冬, 曹学年, 蒋慧灵
湘潭大学数学与计算科学学院, 湘潭 411105
THE IMPLICIT MIDPOINT METHOD FOR TWO-SIDE SPACE FRACTIONAL DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM
Hu Dongdong, Cao Xuenian, Jiang Huiling
School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
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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     
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.
Key wordsTwo-side space fractional diffusion equation   Implicit midpoint method   Quasi-compact difference operator   Stability   Convergence   
收稿日期: 2017-12-14; 出版日期: 2019-08-21
引用本文:   
. 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.
. 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.
 
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