计算数学 ›› 2019, Vol. 41 ›› Issue (3): 295-307.DOI: 10.12286/jssx.2019.3.295

• 论文 • 上一篇    下一篇

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   

  1. 湘潭大学数学与计算科学学院, 湘潭 411105
  • 收稿日期:2017-12-14 出版日期:2019-09-15 发布日期:2019-08-21
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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.

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.

THE IMPLICIT MIDPOINT METHOD FOR TWO-SIDE SPACE FRACTIONAL DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM

Hu Dongdong, Cao Xuenian, Jiang Huiling   

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
  • Received:2017-12-14 Online:2019-09-15 Published:2019-08-21
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.
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
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 words: Two-side space fractional diffusion equation, Implicit midpoint method, Quasi-compact difference operator, Stability, Convergence

MR(2010)主题分类: 

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季刊，创刊于1979年
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