# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1905.01781