An implicit integration factor method for a kind of spatial fractional diffusion equations

TL;DR

This paper develops an implicit integration factor method for spatial fractional diffusion equations, providing a second-order semi-implicit scheme that is accurate even with discontinuous coefficients.

Contribution

The paper introduces a novel second-order implicit integration factor scheme for spatial fractional diffusion equations, enhancing accuracy and efficiency.

Findings

The scheme achieves high accuracy for equations with discontinuous coefficients.

Numerical results validate the effectiveness of the proposed method.

The method is computationally efficient and stable.

Abstract

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.