http://orcid.org/0000-0003-4044-6499
References
- A.A. Alikhanov, A new difference scheme for the time fractional diffusion equation, J. Comput. Phys. 280 (2015), pp. 424–438. doi: 10.1016/j.jcp.2014.09.031
- H.F. Ding and C.P. Li, High-order algorithms for Riesz derivative and their applications (III), Fract. Calc. Appl. Anal. 19 (2016), pp. 19–55. doi: 10.1515/fca-2016-0003
- H.F. Ding and C.P. Li, High-order numerical algorithms for Riesz derivatives via constructing new generating functions. J. Sci. Comput. doi: 10.1007/s10915-016-0317-3.
- H.F. Ding, C.P. Li, and Y.Q. Chen, High-order algorithms for Riesz derivative and their applications (I), Abstr. Appl. Anal. 2014 (2014), pp. 1–17. Article ID 653797.
- H.F. Ding, C.P. Li, and Y.Q. Chen, High-order algorithms for Riesz derivative and their applications (II), J. Comput. Phys. 293 (2015), pp. 218–237. doi: 10.1016/j.jcp.2014.06.007
- V.J. Ervin and J.P. Roop, Variational formulation for the stationary fractional advection dispersion equation, Numer. Methods Partial Differential Equations 22 (2006), pp. 558–576. doi: 10.1002/num.20112
- G.H. Gao, Z.Z. Sun, and H.W. Zhang, A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its application, J. Comput. Phys. 259 (2014), pp. 33–50. doi: 10.1016/j.jcp.2013.11.017
- H. Hejazi, T. Moroney, and F. Liu, A finite volume method for solving the two-sided time-space fractional advection-dispersion equation, Cent. Eur. J. Phys. 11 (2013), pp. 1275–1283.
- C.P. Li, R.F. Wu, and H.F. Ding, High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (I), Commun. Appl. Ind. Math. 6 (2014), pp. 1–32.
- X. Li and C. Xu, A space-time spectral method for the time fractional diffusion equation, SIAM J. Numer. Anal. 47 (2009), pp. 2108–2131. doi: 10.1137/080718942
- Q. Liu, F. Liu, I. Turner, V. Anh, and Y.T. Gu, A RBF meshless approach for modeling a fractal mobile/immobile transport model, Appl. Math. Comput. 226 (2014), pp. 336–347.
- M.M. Meerschaert and C. Tadjeran, Finite difference approximations for fractional advection-dispersion flow equations, J. Comput. Appl. Math. 172 (2004), pp. 65–77. doi: 10.1016/j.cam.2004.01.033
- A. Quarteroni, R. Sacco, and F. Saleri, Numerical Mathematics, Springer, New York, 2007.
- W.Y. Tian, H. Zhou, and W.H. Deng, A class of second order difference approximations for solving space fractional diffusion equations, Math. Comp. 84 (2015), pp. 1703–1727. doi: 10.1090/S0025-5718-2015-02917-2
- Z.B. Wang and S. Vong, Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation, J. Comput. Phys. 277 (2014), pp. 1–15. doi: 10.1016/j.jcp.2014.08.012
- F.H. Zeng, C.P. Li, F.W. Liu, and I. Turner, Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy, SIAM J. Sci. Comput. 37 (2015), pp. A55–A78. doi: 10.1137/14096390X