HIGH-ORDER ALGORITHMS FOR RIESZ DERIVATIVE AND THEIR APPLICATIONS (IV)

被引：7
|
作者：
Ding, Hengfei [1 ]
Li, Changpin [2 ]
机构：
[1] Tianshui Normal Univ, Sch Math & Stat, Tianshui 741001, Peoples R China
[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2019年 / 22卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Riesz derivative; fractional advection-dispersion equation; 4th-order numerical differential formula; finite difference method; DIFFUSION;
D O I：
10.1515/fca-2019-0080
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The main goal of this article is to establish a new 4th-order numerical differential formula to approximate Riesz derivatives which is obtained by means of a newly established generating function. Then the derived formula is used to solve the Riesz space fractional advection-dispersion equation. Meanwhile, by the energy method, it is proved that the difference scheme is unconditionally stable and convergent with order O(T-2 + h(4)). Finally, several numerical examples are given to show that the numerical convergence orders of the numerical differential formulas and the finite difference scheme are in line with the theoretical analysis.
引用
收藏
页码：1537 / 1560
页数：24
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