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A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations
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DOI：10.1016/j.amc.2022.127095.png)
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Abstract
En 中文
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 pre conditioner 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.(c) 2022 Elsevier Inc. All rights reserved.
Keywords:
Time-space fractional equation
Distributed-order fractional derivative
Fast algorithm
Block-circulant-circulant-block
preconditioner
Exponential-sum-approximation method
Stability and convergence
Journal
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3.4
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2.3W
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3.3W