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Article
A Chebyshev pseudo-spectral method to solve the space-time tempered fractional diffusion equation
SIAM Journal on Scientific Computing (2014)
  • Emmanuel Hanert, Universit√© Catholique de Louvain
  • Cecile M Piret, Michigan Technological University
Abstract
The tempered fractional diffusion equation is a generalization of the standard fractional diffusion equation that includes the truncation effects inherent to finite-size physical domains. As such, that equation better describes anomalous transport processes occurring in realistic complex systems. To broaden the range of applicability of tempered fractional diffusion models, efficient numerical methods are needed to solve the model equation. In this work, we have developed a pseudospectral scheme to discretize the space-time fractional diffusion equation with exponential tempering in both space and time. The model solution is expanded in both space and time in terms of Chebyshev polynomials and the discrete equations are obtained with the Galerkin method. Numerical examples are provided to highlight the convergence rate and the flexibility of this approach. The proposed Chebyshev pseudospectral method yields an exponential rate of convergence when the solution is smooth and allows a great flexibility to simultaneously handle fractional time and space derivatives with different levels of truncation. Our results confirm that nonlocal numerical methods are best suited to discretize fractional differential equations as they naturally take the global behavior of the solution into account.
Keywords
  • Chebyshev pseudo-spectral method,
  • fractional derivatives
Publication Date
August 12, 2014
DOI
10.1137/130927292
Publisher Statement
© 2014 Society for Industrial and Applied Mathematics. Deposited in compliance with publisher policies. Publisher's version of record: http://epubs.siam.org/doi/abs/10.1137/130927292
Citation Information
Emmanuel Hanert and Cecile M Piret. "A Chebyshev pseudo-spectral method to solve the space-time tempered fractional diffusion equation" SIAM Journal on Scientific Computing Vol. 36 Iss. 4 (2014) p. A1797 - A1812 ISSN: 1095-7197
Available at: http://works.bepress.com/cecile_piret/1/