A novel implicit finite difference method for the one-dimensional fractional percolation equation

Numerical Algorithms

Volumn 56, Issue 4, 2011, Pages 517-535

  Chen, S ^a   Liu, F ^b   Anh, V ^b  

^a QUANZHOU NORMAL UNIVERSITY   (China)

^b QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Consistency; Convergence; Fractional percolation equation; Implicit finite difference method; Stability

Indexed keywords

EID: 79952279830     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-010-9402-0     Document Type: Article

References (22)

1. Huang, A. X.: A new decomposition for solving percolation equations in porous media. In: 3rd. Int. Symp. on Aerothermodynamics of Internal Flows, Beijing, China, pp. 417-420 (1996).
2. Thusyanthan, N. I., Madabhushi, S. P. G.: Scaling of seepage flow velocity in centrifuge models. CUED/D-SOILS/TR326 (2003).
3. Petford, N., Koenders, M. A.: Seepage flow and consolidation in a deforming porous medium. Geophys. Res. Abstr. 5, 13329 (2003).
4. Chou, H., Lee, B., Chen, C.: The transient infiltration process for seepage flow from cracks. In: Advances in Subsurface Flow and Transport: Eastern and Western Approaches III (2006).
5. He, J.-H.: Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Eng. 167, 57-68 (1998).
6. Miller, K., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993).
7. Podlubny, I.: Fractional Differential Equations. Academic (1999).
8. Samko, S., Kilbas, A., Marichev, O.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach (1993).
9. Huang, F., Liu, F.: The fundamental solution of the space-time fractional advection-dispersion equation. J. Appl. Math. Comput. 19, 233-245 (2005).
10. Liu, F., Anh, V., Turner, I., Zhuang, P.: Time fractional advection dispersion equation. J. Appl. Math. Comput. 13, 233-245 (2003).
11. Liu, F., Anh, V., Turner, I.: Numerical solution of the space fractional Fokker-Planck equation. J. Comp. Appl. Math. 166, 209-219 (2004).
12. Liu, F., Anh, V., Turner, I., Zhuang, P.: Numerical simulation for solute transport in fractal porous media. ANZIAM J. 45(E), 461-473 (2004).
13. Liu, F., Zhuang, P., Anh, V., Turner, I., Burrage, K.: Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation. J. Appl. Math. Comput. 191, 12-21 (2007).
14. Liu, Q., Liu, F., Turner, I., Anh, V.: Approximation of the Lévy-Feller advection-dispersion process by random walk and finite difference method. J. Comput. Phys. 222, 57-70 (2007).
15. Meerschaert, M. M., Tadjeran, C.: Finite difference approximations for fractional advection-dispersion flow equations. J. Comput. Appl. Math. 172, 65-77 (2004).
16. Meerschaert, M. M., Tadjeran, C.: Finite difference approximations for two-sided space-fractional partial differential equations. J. Appl. Numer. Math. 56, 80-90 (2006).
17. Fix, G. J., Roop, J. P.: Least squares finite element solution of a fractional order two-point boundary value problem. J. Comput. Math. Appl. 48, 1017-1033 (2004).
18. d. Numer. Methods for Partial Differ. Equ. 22, 558-576 (2006).
19. Momani, S., Odibat, Z.: Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method. J. Appl. Math. Comput. 177, 488-494 (2006).
20. Varga, R.: Matrix Iterative Analysis. Prentice-Hall (1962).
21. Isaacson, E., Keller, H. B.: Analysis of Numerical Methods. Wiley, New York (1966).
22. Meerschaert, M. M., Scheffler, H. P., Tadjeran, C.: Finite difference methods for two-dimensional fractional dispersion equation. J. Comput. Phys. 211, 249-261 (2006).