On a second order scheme for space fractional diffusion equations with variable coefficients

TL;DR

This paper develops and proves a second order numerical scheme for space fractional diffusion equations with variable coefficients, extending previous work to more general coefficient conditions and validating the scheme with numerical tests.

Contribution

The paper introduces a second order scheme for variable coefficient space fractional diffusion equations and proves its convergence under broader conditions than prior studies.

Findings

Second order convergence is established for the scheme.

The scheme is validated through numerical experiments.

The method applies to more general coefficient conditions.

Abstract

We study a second order scheme for spatial fractional differential equations with variable coefficients. Previous results mainly concentrate on equations with diffusion coefficients that are proportional to each other. In this paper, by further study on the generating function of the discretization matrix, second order convergence of the scheme is proved for diffusion coefficients satisfying a certain condition but are not necessary to be proportional. The theoretical results are justified by numerical tests.