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International Conference on Differential & Difference Equations and Applications

ICDDEA 2015: Differential and Difference Equations with Applications pp 255–263Cite as

Chebyshev Spectral Approximation for Diffusion Equations with Distributed Order in Time

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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 164)

Abstract

In this work we provide a numerical method for the diffusion equation with distributed order in time. The basic idea is to expand the unknown function in Chebyshev polynomials for the time variable t and reduce the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply the method to the forward and backward problems. Some numerical experiments are provided in order to show the performance and accuracy of the proposed method.

Keywords

  • Fractional differential equation
  • Caputo derivative
  • Diffusion equation
  • Chebyshev polynomials
  • Distributed order equation

Mathematics Subject Classification (2000):

  • 26A33
  • 41A50

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Acknowledgements

This work was partially supported by FCT (Portuguese Foundation for Science and Technology) within the projects UID/MAT/00013/2013 (Centro de Matemática) and UID/MAT/00297/2013 (Centro de Matemática e Aplicações).

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Authors and Affiliations

  1. CMAT-Centro de Matemática, Pólo UTAD, Department of Mathematics, University of Trás-os-Montes e Alto Douro UTAD, Quinta de Prados, 5001-801, Vila Real, Portugal

    Maria Luísa Morgado

  2. Centro de Matemática e Aplicações (CMA) and Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal

    Magda Rebelo

Authors
  1. Maria Luísa Morgado
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  2. Magda Rebelo
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Corresponding author

Correspondence to Magda Rebelo .

Editor information

Editors and Affiliations

  1. Departamento de Ciências Exactas e Naturais, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

    Zuzana Došlá

  3. Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

    Ondřej Došlý

  4. School of Mathematics and Stastistics, Huazhong University of Science and Technology, Wuhan, China

    Peter E. Kloeden

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Morgado, M.L., Rebelo, M. (2016). Chebyshev Spectral Approximation for Diffusion Equations with Distributed Order in Time. In: Pinelas, S., Došlá, Z., Došlý, O., Kloeden, P. (eds) Differential and Difference Equations with Applications. ICDDEA 2015. Springer Proceedings in Mathematics & Statistics, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-319-32857-7_24

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