A novel numerical approximation for the space fractional advection-dispersion equation

作者：Shen, S.; Liu, F.^*; Anh, V.; Turner, I.; Chen, J.

来源：IMA Journal of Applied Mathematics, 2014, 79(3): 431-444.

DOI：10.1093/imamat/hxs073

• Riesz fractional advection-dispersion equation
• weighted finite-difference approximation scheme
• Crank-Nicolson scheme
• second-order accurate scheme
• stability
• consistency
• convergence

In this paper, we consider a space fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the first-and second-order space derivatives by the Riesz fractional derivatives of order beta(1) is an element of(0, 1) and beta(2) is an element of(1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference approximation scheme is proposed. When the weighting factor theta equals 1/2, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

• 出版日期2014-6
• 单位集美大学; 华侨大学