Stability and convergence of a finite volume method for the space fractional advection-dispersion equation
暂无分享,去创建一个
[1] L. Gelhar,et al. Field study of dispersion in a heterogeneous aquifer: 2. Spatial moments analysis , 1992 .
[2] I. Podlubny. Fractional differential equations , 1998 .
[3] Fawang Liu,et al. Numerical approximations and solution techniques for the space-time Riesz–Caputo fractional advection-diffusion equation , 2011, Numerical Algorithms.
[4] Fawang Liu,et al. Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation , 2007, Appl. Math. Comput..
[5] Qianqian Yang,et al. Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners , 2013, J. Comput. Phys..
[6] Jing-jun Zhao,et al. A Finite Element Method for the Multiterm Time-Space Riesz Fractional Advection-Diffusion Equations in Finite Domain , 2013 .
[7] Vu Kim Tuan,et al. Extrapolation to the Limit for Numerical Fractional Differentiation , 1995 .
[8] Hong Wang,et al. A fast characteristic finite difference method for fractional advection–diffusion equations , 2011 .
[9] D. Benson,et al. The fractional‐order governing equation of Lévy Motion , 2000 .
[10] Zhaoxia Yang,et al. Finite difference approximations for the fractional advection-diffusion equation , 2009 .
[11] D. Benson,et al. Application of a fractional advection‐dispersion equation , 2000 .
[12] Qianqian Yang,et al. A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation , 2013, Comput. Math. Appl..
[13] M. Meerschaert,et al. Finite difference approximations for fractional advection-dispersion flow equations , 2004 .
[14] David A. Benson,et al. Space‐fractional advection‐dispersion equations with variable parameters: Diverse formulas, numerical solutions, and application to the Macrodispersion Experiment site data , 2007 .
[15] D. Benson,et al. Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications , 2009 .
[16] Fawang Liu,et al. Finite element approximation for a modified anomalous subdiffusion equation , 2011 .
[17] Fawang Liu,et al. Galerkin finite element approximation of symmetric space-fractional partial differential equations , 2010, Appl. Math. Comput..
[18] Fawang Liu,et al. Stability and Convergence of Implicit Numerical Methods for a Class of Fractional Advection-Dispersion Models , 2011 .
[19] M. Meerschaert,et al. Finite difference approximations for two-sided space-fractional partial differential equations , 2006 .
[20] Jingtang Ma,et al. High-order finite element methods for time-fractional partial differential equations , 2011, J. Comput. Appl. Math..
[21] I. Turner,et al. Numerical methods for fractional partial differential equations with Riesz space fractional derivatives , 2010 .
[22] V. Ervin,et al. Variational formulation for the stationary fractional advection dispersion equation , 2006 .
[23] J. Klafter,et al. The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .
[24] V. Ervin,et al. Variational solution of fractional advection dispersion equations on bounded domains in ℝd , 2007 .
[25] J. Crawford,et al. A mass balance based numerical method for the fractional advection‐dispersion equation: Theory and application , 2005 .
[26] Hong Wang,et al. A direct O(N log2 N) finite difference method for fractional diffusion equations , 2010, J. Comput. Phys..
[27] O. Marichev,et al. Fractional Integrals and Derivatives: Theory and Applications , 1993 .
[28] Mark M. Meerschaert,et al. A second-order accurate numerical approximation for the fractional diffusion equation , 2006, J. Comput. Phys..