• 论文 •

### 求解Riesz空间分数阶扩散方程的一种新的数值方法

1. 1. 吕梁学院 数学系, 吕梁 033001;
2. 切斯特大学 数学系, 英国 CH1 4BJ
• 收稿日期:2017-07-28 出版日期:2019-06-15 发布日期:2019-05-18
• 基金资助:

山西省自然科学基金（201801D121010）和吕梁学院校内基金（ZRXN201511）资助项目.

Yang Jinping, Li Zhiqiang, Yan Yubin. A NEW NUMERICAL METHOD FOR SOLVING RIESZ SPACE-FRACTIONAL DIFFUSION EQUATION[J]. Mathematica Numerica Sinica, 2019, 41(2): 170-190.

### A NEW NUMERICAL METHOD FOR SOLVING RIESZ SPACE-FRACTIONAL DIFFUSION EQUATION

Yang Jinping1, Li Zhiqiang1, Yan Yubin2

1. 1. Department of Mathematics, Luliang University, Lvliang 033001, China;
2. Department of Mathematics, University of Chester, Chester CH1 4BJ, UK
• Received:2017-07-28 Online:2019-06-15 Published:2019-05-18

By using Diethelm's method, we construct an approximate scheme to the Riesz space fractional derivative with order O(△x3-α), where 1 < α < 2 and △x denotes the space step size. Further we discretize the time derivative with the Crank-Nicolson method and obtain a new finite difference method for solving Riesz space fractional diffusion equation. The stability and convergence are proved by the matrix method and the error estimate in the maximum norm is O(△t2 + △x3-α), where △t denotes the time step size. Finally, some numerical examples are given to illustrate their correctness and efficiency.
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