Second-order explicit difference schemes for the space fractional advection diffusion equation

作者：Li, Wei^*; Li, Can

来源：Applied Mathematics and Computation, 2015, 257: 446-457.

DOI：10.1016/j.amc.2014.11.030

• Riemann-Liouville fractional derivative
• Fractional advection diffusion equation
• Finite difference scheme
• Stability

In this paper, two kinds of explicit second order difference schemes are developed to solve the space fractional advection diffusion equation. The discretizations of fractional derivatives are based on the weighted and shifted Grunwald difference operators developed in [Meerschaert and Tadjeran, J. Comput.Appl.Math. 172 (2004) 65-77; Tian et al., arXiv: 1201.5949; Li and Deng, arXiv: 1310.7671]. The stability of the presented difference schemes are discussed by means of von Neumann analysis. The analysis shows that the presented numerical schemes are both conditionally stable. The necessary conditions of stability is discussed. Finally, the results of numerical experiments are given to illustrate the performance of the presented numerical methods.

• 出版日期2015-4-15
• 单位西安理工大学; 西北工业大学