An implicit integration factor method for a kind of spatial fractional diffusion equations
It provides an efficient numerical scheme for solving fractional diffusion equations, which are important in modeling anomalous diffusion processes.
The paper develops an implicit integration factor method for spatial fractional diffusion equations, achieving second-order accuracy and handling discontinuous coefficients effectively.
A kind of spatial fractional diffusion equations in this paper are studied. Firstly, an L1 formula is employed for the spatial discretization of the equations. Then, a second order scheme is derived based on the resulting semi-discrete ordinary differential system by using the implicit integration factor method, which is a class of efficient semi-implicit temporal scheme. Numerical results show that the proposed scheme is accurate even for the discontinuous coefficients.