A fast method for variable-order space-fractional diffusion equations

07/05/2019
by   Jinhong Jia, et al.
0

We develop a fast divided-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 approximation does not have a Toeplitz-like structure. In this paper we derive a fast approximation of the coefficient matrix by the means of a sum of Toeplitz matrices multiplied by diagonal matrices. We show that the approximation is asymptotically consistent with the original problem, which requires O(kN^2 N) memory and O(k N^3 N) computational complexity with N and k being the numbers of unknowns and the approximants, respectively. Numerical experiments are presented to demonstrate the effectiveness and the efficiency of the proposed method.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/23/2021

A preconditioner based on sine transform for two-dimensional Riesz space factional diffusion equations in convex domains

In this paper, we develop a fast numerical method for solving the time-d...
research
01/20/2021

Exponential-sum-approximation technique for variable-order time-fractional diffusion equations

In this paper, we study the variable-order (VO) time-fractional diffusio...
research
08/06/2021

Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm

The nonlinear space-fractional problems often allow multiple stationary ...
research
03/23/2021

A fast and oblivious matrix compression algorithm for Volterra integral operators

The numerical solution of dynamical systems with memory requires the eff...
research
08/13/2021

Robust fast method for variable-order time-fractional diffusion equations without regularity assumptions

In this paper, we develop a robust fast method for mobile-immobile varia...

Please sign up or login with your details

Forgot password? Click here to reset