Fractional-Compact Numerical Algorithms for Riesz Spatial Fractional Reaction-Dispersion Equations

It is well known that using high-order numerical algorithms to solve fractional differential equations leads to almost the same computational cost with low-order ones but the accuracy (or convergence order) is greatly improved due to the nonlocal properties of fractional operators. Therefore, develo...

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Veröffentlicht in:Fractional calculus & applied analysis Jg. 20; H. 3; S. 722 - 764
Hauptverfasser: Ding, Hengfei, Li, Changpin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Warsaw Versita 01.06.2017
De Gruyter
Nature Publishing Group
Schlagworte:
65A05
65D15
65D25
65M06
65M12
Abstract Harmonic Analysis
Algorithms
Analysis
Approximation
Computer simulation
Convergence
Derivatives
Differential equations
Dispersion
Energy conversion efficiency
Energy management
fractional-compact numerical approximation formula
Functional Analysis
generating function
Integral Transforms
Mathematical analysis
Mathematics
Operational Calculus
Research Paper
Riesz derivative
Riesz spatial fractional reaction-dispersion equation
Riesz derivative
65A05
65M06
fractional-compact numerical approximation formula
generating function
65D25
65D15
Riesz spatial fractional reaction-dispersion equation
65M12
ISSN:1311-0454, 1314-2224
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:It is well known that using high-order numerical algorithms to solve fractional differential equations leads to almost the same computational cost with low-order ones but the accuracy (or convergence order) is greatly improved due to the nonlocal properties of fractional operators. Therefore, developing some high-order numerical approximation formulas for fractional derivatives plays a more important role in numerically solving fractional differential equations. This paper focuses on constructing (generalized) high-order fractional-compact numerical approximation formulas for Riesz derivatives. Then we apply the developed formulas to the one- and two-dimension Riesz spatial fractional reaction-dispersion equations. The stability and convergence of the derived numerical algorithms are strictly studied by using the energy analysis method. Finally, numerical simulations are given to demonstrate the efficiency and convergence orders of the presented numerical algorithms.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1311-0454
1314-2224
DOI:10.1515/fca-2017-0038