SIAM Journal on Numerical Analysis
A Fourier method for the fractional diffusion equation describing sub-diffusion
Journal of Computational Physics
Finite difference approximations for a fractional advection diffusion problem
Journal of Computational Physics
Explicit methods for fractional differential equations and their stability properties
Journal of Computational and Applied Mathematics
On some explicit Adams multistep methods for fractional differential equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Compact finite difference method for the fractional diffusion equation
Journal of Computational Physics
On accurate product integration rules for linear fractional differential equations
Journal of Computational and Applied Mathematics
Numerical approaches to fractional calculus and fractional ordinary differential equation
Journal of Computational Physics
Computers & Mathematics with Applications
Numerical approximations for fractional diffusion equations via splines
Computers & Mathematics with Applications
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In this paper, we develop two classes of finite difference schemes for the reaction-subdiffusion equations by using a mixed spline function in space direction, forward and backward difference in time direction, respectively. It has been shown that some of the previous known difference schemes can be derived from our schemes if we suitably choose the spline parameters. By Fourier method, we prove that one class of difference scheme is unconditionally stable and convergent, the other is conditionally stable and convergent. Finally, some numerical results are provided to demonstrate the effectiveness of the proposed difference schemes.