Iterative solution methods
Conjugate Gradient Methods for Toeplitz Systems
SIAM Review
Multigrid Method for Ill-Conditioned Symmetric Toeplitz Systems
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Numerical solution of the space fractional Fokker-Planck equation
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
Finite difference approximations for fractional advection-dispersion flow equations
Journal of Computational and Applied Mathematics
The accuracy and stability of an implicit solution method for the fractional diffusion equation
Journal of Computational Physics
Finite difference methods for two-dimensional fractional dispersion equation
Journal of Computational Physics
A second-order accurate numerical approximation for the fractional diffusion equation
Journal of Computational Physics
Numerical Approximation of a Time Dependent, Nonlinear, Space-Fractional Diffusion Equation
SIAM Journal on Numerical Analysis
Finite difference/spectral approximations for the time-fractional diffusion equation
Journal of Computational Physics
An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)
An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)
Numerical solutions for fractional reaction-diffusion equations
Computers & Mathematics with Applications
Implicit finite difference approximation for time fractional diffusion equations
Computers & Mathematics with Applications
Finite difference approximations for a fractional advection diffusion problem
Journal of Computational Physics
Compact finite difference method for the fractional diffusion equation
Journal of Computational Physics
Finite difference approximations for two-sided space-fractional partial differential equations
Applied Numerical Mathematics
Finite Element Method for the Space and Time Fractional Fokker-Planck Equation
SIAM Journal on Numerical Analysis
A direct O(Nlog2N) finite difference method for fractional diffusion equations
Journal of Computational Physics
A characteristic difference method for the transient fractional convection-diffusion equations
Applied Numerical Mathematics
Multigrid method for fractional diffusion equations
Journal of Computational Physics
Journal of Computational Physics
Fractional-Order Anisotropic Diffusion for Image Denoising
IEEE Transactions on Image Processing
A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations
Journal of Computational Physics
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In this paper, we are concerned with numerical methods for the solution of initial-boundary value problems of anomalous diffusion equations of order @a@?(1,2). The classical Crank-Nicholson method is used to discretize the fractional diffusion equation and then the spatial extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Two preconditioned iterative methods, namely, the preconditioned generalized minimal residual (preconditioned GMRES) method and the preconditioned conjugate gradient for normal residual (preconditioned CGNR) method, are proposed to solve relevant linear systems. Numerical experiments are given to illustrate the efficiency of the methods.