A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation

摘要：

In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the first-order and second-order space derivatives by the Riesz fractional derivatives of order β1∈(0,1) and β2∈(1; 2, respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional finite difference approximation scheme is proposed. When the weighting factor θ = 1=2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. 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.

关键词： Riesz fractional advection-dispersion equation weighted finite difference approximation scheme Crank-Nicolson scheme second-order accurate stability consistency convergence.

作者: S. Shen F. Liu V. Anh I. Turner J. Chen

作者单位: hool of Mathematical Sciences, Huaqiao University, Quanzhou,Fujian, China School of Mathematical Sciences, Queensland University ofTechnology, GPO Box 2434, Brisbane, Qld. 40 College of Mathematics , Jimei University, Xiamen, Fujian, China

会议类型: 国际会议

会议名称: The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)

会议地点: 南京

会议语种:英文

页码: 1-7

在线出版日期: 2012-05-14（万方平台首次上网日期，不代表论文的发表时间）