High-order algorithms for riesz derivative and their applications (IV)

被引：0
|
作者：
Hengfei Ding
Changpin Li
机构：
[1] Tianshui Normal University,School of Mathematics and Statistics
[2] Shanghai University Shanghai,Department of Mathematics
来源：
Fractional Calculus and Applied Analysis | 2019年 / 22卷
关键词：
65A05; 65D15; 65D25; 65M06; 65M12; Riesz derivative; fractional advection-dispersion equation; 4th-order numerical differential formula; finite difference method;
D O I：
暂无
中图分类号：
学科分类号：
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(τ2 + h4). 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.
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页码：1537 / 1560
页数：23
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