 An α-robust fast algorithm for distributed-order time–space fractional diffusion equation with weakly singular solutionLu-Yao Sun, Siu-Long Lei, Hai-Wei Sun and Jia-Li Zhang Mathematics and Computers in Simulation (MATCOM), 2023, vol. 207, issue C, 437-452 Abstract: A fast algorithm is proposed for solving two-dimensional distributed-order time–space fractional diffusion equation where the solution has a weak singularity at initial time. The distributed-order fractional problem is firstly transformed into multi-term fractional problem by the Gauss–Legendre quadrature formula. Then the exponential-sum-approximation method on graded mesh is utilized to discretize time Caputo fractional derivatives in time direction, and a standard finite difference method is employed to approximate the spatial Riesz fractional derivatives. The scheme is proved to be α-robust convergent analytically. The discrete linear system possesses symmetric positive definite block-Toeplitz–Toeplitz-block structure and is efficiently solved by conjugate gradient method with the state-of-the-art sine-transformed based preconditioner. Numerical examples confirm the error analysis and the effectiveness of the preconditioner. Keywords: Distributed-order time–space fractional equation; Singularity; Sine transform based preconditioner; Exponential-sum-approximation method; α-robust (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:207:y:2023:i:c:p:437-452 DOI: 10.1016/j.matcom.2023.01.011 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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