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

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5 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