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A Numerical Method for the Solution of the Time-Fractional Diffusion Equation

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Computational Science and Its Applications – ICCSA 2014 (ICCSA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8579))

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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.

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Author information

Authors and Affiliations

  1. University of Minho, Campus de Azurém, 4800-058, Guimarães, Portugal

    Luis L. Ferrás

  2. Department of Mathematics, University of Chester, CH1 4BJ, UK

    Luis L. Ferrás & Neville J. Ford

  3. CM-UTAD, Department of Mathematics, University of Trás-os-Montes e Alto Douro, UTAD, Quinta de Prados, 5001-801, Vila Real, Portugal

    Maria L. Morgado

  4. Department of Mathematics, Facudade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal

    Magda Rebelo

Authors
  1. Luis L. Ferrás
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  2. Neville J. Ford
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  3. Maria L. Morgado
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  4. Magda Rebelo
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Editor information

Editors and Affiliations

  1. School of Engineering, University of Basilicata, 85100, Potenza, Italy

    Beniamino Murgante

  2. Department of Computer and Information Sciences, Covenant University, Ota, Nigeria

    Sanjay Misra

  3. Department of Production and Systems, University of Minho, 4710-057, Braga, Portugal

    Ana Maria A. C. Rocha

  4. DICAR, Polytecnico di Bari, 70125, Bari, Italy

    Carmelo Torre

  5. University of Minho, Braga, Portugal

    Jorge Gustavo Rocha  & Maria Irene Falcão  & 

  6. Monash University, 3800, Clayton, VIC, Australia

    David Taniar

  7. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, 813-8503, Higashi-ku, Fukuoka, Japan

    Bernady O. Apduhan

  8. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

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Ferrás, L.L., Ford, N.J., Morgado, M.L., Rebelo, M. (2014). A Numerical Method for the Solution of the Time-Fractional Diffusion Equation. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8579. Springer, Cham. https://doi.org/10.1007/978-3-319-09144-0_9

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  • DOI: https://doi.org/10.1007/978-3-319-09144-0_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09143-3

  • Online ISBN: 978-3-319-09144-0

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