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A fast method for variable-order space-fractional diffusion equations
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Journal Article
A fast method for variable-order space-fractional diffusion equations
2020
Overview
We develop a fast divide-and-conquer indirect collocation method for the homogeneous Dirichlet boundary value problem of variable-order space-fractional diffusion equations. Due to the impact of the space-dependent variable order, the resulting stiffness matrix of the numerical scheme does not have a Toeplitz structure. In this paper, we derive a fast approximation of the coefficient matrix by the means of a finite sum of Toeplitz matrices multiplied by diagonal matrices. We show that the approximation is asymptotically consistent with the original problem, which requires
O
(
N
log
2
N
)
memory and
O
(
N
log
3
N
)
computational complexity with
N
being the numbers of unknowns. Numerical experiments are presented to demonstrate the effectiveness and the efficiency of the proposed method.
Publisher
Springer US,Springer Nature B.V
Subject
