A numerical method for the solution of the time-fractional diffusion equation

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

In this work we provide a new numerical scheme for the solution of the fractional sub-diffusion equation. This new scheme is based on a combination of a recently proposed non-polynomial collocation method for fractional ordinary differential equations and the method of lines. A comparison of the numerical results obtained with known analytical solutions is carried out, using different values of the order of the fractional derivative and several time and space stepsizes, and we conclude that, as in the fractional ordinary differential equation case, the convergence order of the method is independent of the order of the time derivative and does not decrease when dealing with certain nonsmooth solutions.
Original languageUnknown
Title of host publicationLecture Notes in Computer Science
EditorsB. Murgante, S. Misra, A. M. A. C. Rocha, C. Torre, J.G. Rocha, M. I. Falcão, D. Taniar, B. O. Apduhan, O. Gervasi
Place of PublicationSwitzerland
PublisherSpringer International Publishing
Pages117-131
ISBN (Electronic)978-3-319-09144-0
ISBN (Print)978-3-319-09143-3
DOIs
Publication statusPublished - 1 Jan 2014
Event14th International Conference on Computational Science and Its Applications (ICCSA) -
Duration: 1 Jan 2014 → …

Conference

Conference14th International Conference on Computational Science and Its Applications (ICCSA)
Period1/01/14 → …

Cite this

Rebelo, M. S. D. J. (2014). A numerical method for the solution of the time-fractional diffusion equation. In B. Murgante, S. Misra, A. M. A. C. Rocha, C. Torre, J. G. Rocha, M. I. Falcão, D. Taniar, B. O. Apduhan, ... O. Gervasi (Eds.), Lecture Notes in Computer Science (pp. 117-131). Switzerland: Springer International Publishing. https://doi.org/10.1007/978-3-319-09144-0_9
Rebelo, Magda Stela de Jesus. / A numerical method for the solution of the time-fractional diffusion equation. Lecture Notes in Computer Science. editor / B. Murgante ; S. Misra ; A. M. A. C. Rocha ; C. Torre ; J.G. Rocha ; M. I. Falcão ; D. Taniar ; B. O. Apduhan ; O. Gervasi. Switzerland : Springer International Publishing, 2014. pp. 117-131
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title = "A numerical method for the solution of the time-fractional diffusion equation",
abstract = "In this work we provide a new numerical scheme for the solution of the fractional sub-diffusion equation. This new scheme is based on a combination of a recently proposed non-polynomial collocation method for fractional ordinary differential equations and the method of lines. A comparison of the numerical results obtained with known analytical solutions is carried out, using different values of the order of the fractional derivative and several time and space stepsizes, and we conclude that, as in the fractional ordinary differential equation case, the convergence order of the method is independent of the order of the time derivative and does not decrease when dealing with certain nonsmooth solutions.",
keywords = "Caputo derivative, method of lines, nonpolynomial collocation method, subdiffusionequation, fractional differential equations",
author = "Rebelo, {Magda Stela de Jesus}",
year = "2014",
month = "1",
day = "1",
doi = "10.1007/978-3-319-09144-0_9",
language = "Unknown",
isbn = "978-3-319-09143-3",
pages = "117--131",
editor = "B. Murgante and S. Misra and Rocha, {A. M. A. C.} and C. Torre and J.G. Rocha and Falc{\~a}o, {M. I.} and D. Taniar and Apduhan, {B. O.} and O. Gervasi",
booktitle = "Lecture Notes in Computer Science",
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Rebelo, MSDJ 2014, A numerical method for the solution of the time-fractional diffusion equation. in B Murgante, S Misra, AMAC Rocha, C Torre, JG Rocha, MI Falcão, D Taniar, BO Apduhan & O Gervasi (eds), Lecture Notes in Computer Science. Springer International Publishing, Switzerland, pp. 117-131, 14th International Conference on Computational Science and Its Applications (ICCSA), 1/01/14. https://doi.org/10.1007/978-3-319-09144-0_9

A numerical method for the solution of the time-fractional diffusion equation. / Rebelo, Magda Stela de Jesus.

Lecture Notes in Computer Science. ed. / B. Murgante; S. Misra; A. M. A. C. Rocha; C. Torre; J.G. Rocha; M. I. Falcão; D. Taniar; B. O. Apduhan; O. Gervasi. Switzerland : Springer International Publishing, 2014. p. 117-131.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - A numerical method for the solution of the time-fractional diffusion equation

AU - Rebelo, Magda Stela de Jesus

PY - 2014/1/1

Y1 - 2014/1/1

N2 - In this work we provide a new numerical scheme for the solution of the fractional sub-diffusion equation. This new scheme is based on a combination of a recently proposed non-polynomial collocation method for fractional ordinary differential equations and the method of lines. A comparison of the numerical results obtained with known analytical solutions is carried out, using different values of the order of the fractional derivative and several time and space stepsizes, and we conclude that, as in the fractional ordinary differential equation case, the convergence order of the method is independent of the order of the time derivative and does not decrease when dealing with certain nonsmooth solutions.

AB - In this work we provide a new numerical scheme for the solution of the fractional sub-diffusion equation. This new scheme is based on a combination of a recently proposed non-polynomial collocation method for fractional ordinary differential equations and the method of lines. A comparison of the numerical results obtained with known analytical solutions is carried out, using different values of the order of the fractional derivative and several time and space stepsizes, and we conclude that, as in the fractional ordinary differential equation case, the convergence order of the method is independent of the order of the time derivative and does not decrease when dealing with certain nonsmooth solutions.

KW - Caputo derivative

KW - method of lines

KW - nonpolynomial collocation method

KW - subdiffusionequation

KW - fractional differential equations

U2 - 10.1007/978-3-319-09144-0_9

DO - 10.1007/978-3-319-09144-0_9

M3 - Conference contribution

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BT - Lecture Notes in Computer Science

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A2 - Misra, S.

A2 - Rocha, A. M. A. C.

A2 - Torre, C.

A2 - Rocha, J.G.

A2 - Falcão, M. I.

A2 - Taniar, D.

A2 - Apduhan, B. O.

A2 - Gervasi, O.

PB - Springer International Publishing

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Rebelo MSDJ. A numerical method for the solution of the time-fractional diffusion equation. In Murgante B, Misra S, Rocha AMAC, Torre C, Rocha JG, Falcão MI, Taniar D, Apduhan BO, Gervasi O, editors, Lecture Notes in Computer Science. Switzerland: Springer International Publishing. 2014. p. 117-131 https://doi.org/10.1007/978-3-319-09144-0_9