A banded preconditioning iteration method for time-space fractional advection-diffusion equations
type: Item
instance of: scholarly article
title: A banded preconditioning iteration method for time-space fractional advection-diffusion equations
zbMATH Open document ID: 1427.65221
DOI: 10.1155/2017/6961296
author: Minli Zeng
author: Guo-Feng Zhang
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: In this paper, we concentrate on the efficient solvers for the time-space fractional advection-diffusion equations. Firstly, the implicit finite difference schemes with the shifted Grünwald-Letnikov approximations for spatial fractional derivative and unshifted Grünwald-Letnikov approximations for time fractional derivative are employed to discretize time-space fractional advection-diffusion equations. The discretization results in a series of large dense linear systems. Then, a banded preconditioner is proposed and some theoretical properties for the preconditioning matrix are studied. Numerical implementations show that the banded preconditioner may lead to satisfactory experimental results when we choose appropriate bandwidth in the preconditioner.
Mathematics Subject Classification ID: 65M22
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6972406
Wikidata QID: Q59147734
describes a project that uses: ma2dfc
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/6961296
OpenAlex ID: W2582538157
cites work: Matrix approach to discrete fractional calculus. II: Partial fractional differential equations
cites work: The random walk's guide to anomalous diffusion: A fractional dynamics approach
cites work: Waiting-times and returns in high-frequency financial data: An empirical study
cites work: A novel solution for pressure drop in singly connected microchannels of arbitrary cross-section
cites work: Q4941491
cites work: Finite difference approximations for two-sided space-fractional partial differential equations
cites work: A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
cites work: Multigrid method for fractional diffusion equations
cites work: A circulant preconditioner for fractional diffusion equations
cites work: Circulant and skew-circulant splitting iteration for fractional advection–diffusion equations
cites work: Compact finite difference method for the fractional diffusion equation
cites work: Finite difference/spectral approximations for the time-fractional diffusion equation
cites work: Finite difference approximations for a fractional advection diffusion problem
cites work: Preconditioned iterative methods for fractional diffusion equation
cites work: Approximate Inverse Circulant-plus-Diagonal Preconditioners for Toeplitz-plus-Diagonal Matrices
cites work: Preconditioning Techniques for Diagonal-times-Toeplitz Matrices in Fractional Diffusion Equations
cites work: A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations
cites work: Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
cites work: On a Hermitian and skew-Hermitian splitting iteration method for continuous Sylvester equations
cites work: Explicit Solutions of Linear Matrix Equations
cites work: The Spectrum of a Family of Circulant Preconditioned Toeplitz Systems
description: scientific article; zbMATH DE number 6972406