Block iterative algorithms for solving Hermite bicubic collocation equations
SIAM Journal on Numerical Analysis
Discrete-time Orthogonal Spline Collocation Methods for Schrödinger Equations in Two Space Variables
SIAM Journal on Numerical Analysis
Orthogonal spline collocation methods for partial differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
The accuracy and stability of an implicit solution method for the fractional diffusion equation
Journal of Computational Physics
A second-order accurate numerical approximation for the fractional diffusion equation
Journal of Computational Physics
Weighted average finite difference methods for fractional diffusion equations
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
SIAM Journal on Numerical Analysis
Compact finite difference method for the fractional diffusion equation
Journal of Computational Physics
A fully discrete difference scheme for a diffusion-wave system
Applied Numerical Mathematics
Finite Element Method for the Space and Time Fractional Fokker-Planck Equation
SIAM Journal on Numerical Analysis
Hi-index | 7.29 |
We develop two kinds of numerical schemes to efficiently solve the subdiffusion equation, which is used to describe anomalous subdiffusive transport processes. The time fractional derivative is first discretized by L1-approximation and the Grunwald-Letnikov approximation, respectively. Then we use the orthogonal spline collocation method to approximate the two semi-discretized subdiffusion equations. The stability and convergence of time semi-discretization and full discretization schemes are both established strictly for the two schemes. Both of them are unconditionally stable. Numerically the convergent orders in space (including the solution and its first derivative) are four for the Hermite cubic spline approximation, and theoretically we get that at least the solution itself has a fourth order convergent rate. Extensive numerical results are presented to show the convergent order and robustness of the numerical schemes.