A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations

Lu-Yao Sun, Zhi-Wei Fang, Siu-Long Lei, Hai-Wei Sun and Jia-Li Zhang

Applied Mathematics and Computation, 2022, vol. 425, issue C

Abstract: In this paper, a fast algorithm is proposed for solving distributed-order time-space fractional diffusion equations. Integral terms in time and space directions are discretized by the Gauss-Legendre quadrature formula. The Caputo fractional derivatives are approximated by the exponential-sum-approximation method, and the finite difference method is applied for spatial approximation. The coefficient matrix of the discretized linear system is symmetric positive definite and possesses block-Toeplitz-Toeplitz-block structure. The preconditioned conjugate gradient method with a block-circulant-circulant-block preconditioner is employed to solve the linear system. Theoretically, the stability and convergence of the proposed scheme are discussed. Numerical experiments are carried out to demonstrate the effectiveness of the scheme.

Keywords: Time-space fractional equation; Distributed-order fractional derivative; Fast algorithm; Block-circulant-circulant-block preconditioner; Exponential-sum-approximation method; Stability and convergence (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300322001795
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001795

DOI: 10.1016/j.amc.2022.127095

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().