On a second order scheme for space fractional diffusion equations with variable coefficients
For researchers in numerical analysis and computational fractional PDEs, this extends the applicability of a second-order scheme to a broader class of variable-coefficient problems.
The paper proves second-order convergence for a numerical scheme solving space-fractional diffusion equations with variable coefficients, relaxing the previous requirement that diffusion coefficients be proportional. Numerical tests confirm the theoretical results.
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.