Numerical methods for the solution of partial differential equations of fractional order

V. E. Lynch; B. A. Carreras; D. del-Castillo-Negrete; K. M. Ferreira-Mejias; H. R. Hicks

doi:10.1016/j.jcp.2003.07.008

Numerical methods for the solution of partial differential equations of fractional order

V. E. Lynch, B. A. Carreras, D. del-Castillo-Negrete, K. M. Ferreira-Mejias, H. R. Hicks

Plasma Theory and Modeling

Research output: Contribution to journal › Article › peer-review

223 Scopus citations

Abstract

Anomalous diffusion is a possible mechanism underlying plasma transport in magnetically confined plasmas. To model this transport mechanism, fractional order space derivative operators can be used. Here, the numerical properties of partial differential equations of fractional order α, 1 ≤ α ≤ 2, are studied. Two numerical schemes, an explicit and a semi-implicit one, are used in solving these equations. Two different discretization methods of the fractional derivative operator have also been used. The accuracy and stability of these methods are investigated for several standard types of problems involving partial differential equations of fractional order.

Original language	English
Pages (from-to)	406-421
Number of pages	16
Journal	Journal of Computational Physics
Volume	192
Issue number	2
DOIs	https://doi.org/10.1016/j.jcp.2003.07.008
State	Published - Dec 10 2003

Funding

This research is sponsored by Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy under contract number DE-AC05-00OR22725. K.M.F. was supported by the Energy Research Undergraduate Laboratory Fellowship program of the U.S. Department of Energy.

Funders	Funder number
U.S. Department of Energy	DE-AC05-00OR22725
Oak Ridge National Laboratory

Keywords

Anomalous diffusion
Fractional derivatives
Partial differential equations
Plasma transport

Access to Document

10.1016/j.jcp.2003.07.008

Cite this

@article{70c42bd4f3ef4e64b204a75ab12ed5c8,

title = "Numerical methods for the solution of partial differential equations of fractional order",

abstract = "Anomalous diffusion is a possible mechanism underlying plasma transport in magnetically confined plasmas. To model this transport mechanism, fractional order space derivative operators can be used. Here, the numerical properties of partial differential equations of fractional order α, 1 ≤ α ≤ 2, are studied. Two numerical schemes, an explicit and a semi-implicit one, are used in solving these equations. Two different discretization methods of the fractional derivative operator have also been used. The accuracy and stability of these methods are investigated for several standard types of problems involving partial differential equations of fractional order.",

keywords = "Anomalous diffusion, Fractional derivatives, Partial differential equations, Plasma transport",

author = "Lynch, {V. E.} and Carreras, {B. A.} and D. del-Castillo-Negrete and Ferreira-Mejias, {K. M.} and Hicks, {H. R.}",

year = "2003",

month = dec,

day = "10",

doi = "10.1016/j.jcp.2003.07.008",

language = "English",

volume = "192",

pages = "406--421",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - Numerical methods for the solution of partial differential equations of fractional order

AU - Lynch, V. E.

AU - Carreras, B. A.

AU - del-Castillo-Negrete, D.

AU - Ferreira-Mejias, K. M.

AU - Hicks, H. R.

PY - 2003/12/10

Y1 - 2003/12/10

N2 - Anomalous diffusion is a possible mechanism underlying plasma transport in magnetically confined plasmas. To model this transport mechanism, fractional order space derivative operators can be used. Here, the numerical properties of partial differential equations of fractional order α, 1 ≤ α ≤ 2, are studied. Two numerical schemes, an explicit and a semi-implicit one, are used in solving these equations. Two different discretization methods of the fractional derivative operator have also been used. The accuracy and stability of these methods are investigated for several standard types of problems involving partial differential equations of fractional order.

AB - Anomalous diffusion is a possible mechanism underlying plasma transport in magnetically confined plasmas. To model this transport mechanism, fractional order space derivative operators can be used. Here, the numerical properties of partial differential equations of fractional order α, 1 ≤ α ≤ 2, are studied. Two numerical schemes, an explicit and a semi-implicit one, are used in solving these equations. Two different discretization methods of the fractional derivative operator have also been used. The accuracy and stability of these methods are investigated for several standard types of problems involving partial differential equations of fractional order.

KW - Anomalous diffusion

KW - Fractional derivatives

KW - Partial differential equations

KW - Plasma transport

UR - http://www.scopus.com/inward/record.url?scp=0345448323&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2003.07.008

DO - 10.1016/j.jcp.2003.07.008

M3 - Article

AN - SCOPUS:0345448323

SN - 0021-9991

VL - 192

SP - 406

EP - 421

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 2

ER -

Numerical methods for the solution of partial differential equations of fractional order

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this