An α-robust fast algorithm for distributed-order time–space fractional diffusion equation with weakly singular solution

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 quad...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics and computers in simulation Vol. 207; pp. 437 - 452
Main Authors: Sun, Lu-Yao, Lei, Siu-Long, Sun, Hai-Wei, Zhang, Jia-Li
Format: Journal Article
Language:English
Published: Elsevier B.V 01.05.2023
Subjects:
[formula omitted]-robust
Distributed-order time–space fractional equation
Exponential-sum-approximation method
Sine transform based preconditioner
Singularity
Singularity
Sine transform based preconditioner
Distributed-order time–space fractional equation
Exponential-sum-approximation method
α-robust
ISSN:0378-4754, 1872-7166
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2023.01.011