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Article
A Fast Algorithm for Solving the Space-Time Fractional Diffusion Equation
Computers and Mathematics with Applications
  • Siwei Duo
  • Lili Ju
  • Yanzhi Zhang, Missouri University of Science and Technology
Abstract

In this paper, we propose a fast algorithm for efficient and accurate solution of the space-time fractional diffusion equations defined in a rectangular domain. The spatial discretization is done by using the central finite difference scheme and matrix transfer technique. Due to its nonlocality, numerical discretization of the spectral fractional Laplacian (−Δ)sα/2 results in a large dense matrix. This causes considerable challenges not only for storing the matrix but also for computing matrix-vector products in practice. By utilizing the compact structure of the discrete system and the discrete sine transform, our algorithm avoids to store the large matrix from discretizing the nonlocal operator and also significantly reduces the computational costs. We then use the Laplace transform method for time integration of the semi-discretized system and a weighted trapezoidal method to numerically compute the convolutions needed in the resulting scheme. Various experiments are presented to demonstrate the efficiency and accuracy of our method.

Department(s)
Mathematics and Statistics
Keywords and Phrases
  • Caputo fractional derivative,
  • Discrete sine transform,
  • Fractional diffusion equation,
  • Matrix transfer method,
  • Matrix-vector product,
  • Spectral fractional Laplacian
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2018 Elsevier Ltd, All rights reserved.
Publication Date
3-1-2018
Citation Information
Siwei Duo, Lili Ju and Yanzhi Zhang. "A Fast Algorithm for Solving the Space-Time Fractional Diffusion Equation" Computers and Mathematics with Applications Vol. 75 Iss. 6 (2018) p. 1929 - 1941 ISSN: 0898-1221
Available at: http://works.bepress.com/yanzhi-zhang/27/