Matrix analysis
Discretized fractional calculus
SIAM Journal on Mathematical Analysis
Numerical methods for the solution of partial differential equations of fractional order
Journal of Computational Physics
Finite difference approximations for fractional advection-dispersion flow equations
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
The accuracy and stability of an implicit solution method for the fractional diffusion equation
Journal of Computational Physics
A second-order accurate numerical method for the two-dimensional fractional diffusion equation
Journal of Computational Physics
Finite difference/spectral approximations for the time-fractional diffusion equation
Journal of Computational Physics
A Fourier method for the fractional diffusion equation describing sub-diffusion
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Numerical treatment of fractional heat equations
Applied Numerical Mathematics
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
Matrix approach to discrete fractional calculus II: Partial fractional differential equations
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Explicit and implicit finite difference schemes for fractional Cattaneo equation
Journal of Computational Physics
A direct O(Nlog2N) finite difference method for fractional diffusion equations
Journal of Computational Physics
A compact finite difference scheme for the fractional sub-diffusion equations
Journal of Computational Physics
A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
The Grünwald-Letnikov method for fractional differential equations
Computers & Mathematics with Applications
Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Multigrid method for fractional diffusion equations
Journal of Computational Physics
Compact alternating direction implicit method for two-dimensional time fractional diffusion equation
Journal of Computational Physics
Journal of Computational Physics
Error Estimates of Crank-Nicolson-Type Difference Schemes for the Subdiffusion Equation
SIAM Journal on Numerical Analysis
Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Boundary particle method for Laplace transformed time fractional diffusion equations
Journal of Computational Physics
A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations
Journal of Computational Physics
Mixed spline function method for reaction-subdiffusion equations
Journal of Computational Physics
A high-order compact exponential scheme for the fractional convection-diffusion equation
Journal of Computational and Applied Mathematics
Orthogonal spline collocation methods for the subdiffusion equation
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Preconditioned iterative methods for fractional diffusion equation
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.52 |
High-order compact finite difference scheme for solving one-dimensional fractional diffusion equation is considered in this paper. After approximating the second-order derivative with respect to space by the compact finite difference, we use the Grunwald-Letnikov discretization of the Riemann-Liouville derivative to obtain a fully discrete implicit scheme. We analyze the local truncation error and discuss the stability using the Fourier method, then we prove that the compact finite difference scheme converges with the spatial accuracy of fourth order using matrix analysis. Numerical results are provided to verify the accuracy and efficiency of the proposed algorithm.