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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia


IMPACT FACTOR 2018: 3.514
5-year IMPACT FACTOR: 3.524

CiteScore 2018: 3.44

SCImago Journal Rank (SJR) 2018: 1.891
Source Normalized Impact per Paper (SNIP) 2018: 1.808

Mathematical Citation Quotient (MCQ) 2018: 1.08

Online
ISSN
1314-2224
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Volume 22, Issue 6

Issues

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

Hengfei Ding / Changpin Li
Published Online: 2019-12-31 | DOI: https://doi.org/10.1515/fca-2019-0080

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 đť“ž(Ď„2 + 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.

MSC 2010: 65A05; 65D15; 65D25; 65M06; 65M12

Key Words and Phrases: Riesz derivative; fractional advection-dispersion equation; 4th-order numerical differential formula; finite difference method

This paper is dedicated to the memory of late Professor Wen Chen

References

About the article

Received: 2019-04-15

Published Online: 2019-12-31

Published in Print: 2019-12-18


Citation Information: Fractional Calculus and Applied Analysis, Volume 22, Issue 6, Pages 1537–1560, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2019-0080.

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