High-order algorithms for riesz derivative and their applications (IV)-Reference-Cited by-同舟云学术

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

Published:2019-12-01 Issue:6 Volume:22 Page:1537-1560
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Ding Hengfei¹,Li Changpin²

Affiliation:

1. School of Mathematics and Statistics , Tianshui Normal University , Tianshui , 741001 , China

2. Department of Mathematics , Shanghai University Shanghai , Shanghai , 200444 , China

Abstract

Abstract 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(τ 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2019-0080/pdf

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