[1]
|
M. Giona and H. E. Roman, “Fractional Diffusion Equation for Transport Phenomena in Random Media,” Journal of Physics A, Vol. 185, No. 1-4, 1992, pp. 87-97.
|
[2]
|
R. Metzler, J. Klafter and I. M. Sokolov, “Anomalous Transport in External Fields: Continuous Time Random Walks and Fractional Diffusion Equations Extends,” Physical Review E, Vol. 58, No. 3, 1998, pp. 1621-1633. http://dx.doi.org/10.1103/PhysRevE.58.1621
|
[3]
|
R. Metzler and J. Klafter, “Boundary Value Problems for Fractional Diffusion Equations,” Journal of Physics A, Vol. 278, No. 1-2, 2000, pp. 107-125.
|
[4]
|
B. I. Henry and S. L. Wearne, “Fractional Reaction-Diffusion,” Journal of Physics A, Vol. 276, No. 3-4, 2000, pp. 448-445.
|
[5]
|
Y. Zhang, M. Meerschaert and B. Baeumer, “Particle Tracking for Time-Fractional Diffusion,” Physical Review E, Vol. 78, No. 3, 2008, Article ID: 036705.
|
[6]
|
H. G. Sun, W. Chen and Y. Q. Chen, “Variable-Order Fractional Differential Operators in Anomalous Diffusion Modeling,” Journal of Physics A, Vol. 338, No. 21, 2009, pp. 4586-4592.
|
[7]
|
A. T. M. Langlands and B. I. Henry, “The Accuracy and Stability of an Implicit Solution Method for the Fractional Diffusion Equation,” Journal of Computational Physics, Vol. 205, No. 2, 2005, pp. 719-736. http://dx.doi.org/10.1016/j.jcp.2004.11.025
|
[8]
|
S. B. Yuste and L. Acedo, “On an Explicit Finite Difference Method for Fractional Diffusion Equations,” SIAM Journal on Numerical Analysis, Vol. 42, No. 5, 2005, pp. 1862-1874. http://dx.doi.org/10.1137/030602666
|
[9]
|
S. B. Yuste, “Weighted Average Finite Difference Methods for Fractional Diffusion Equations,” Journal of Computational Physics, Vol. 216, No. 1, 2006, pp. 264-274. http://dx.doi.org/10.1016/j.jcp.2005.12.006
|
[10]
|
C. Tadjeran, M. M. Meerschaert and H.-P. Scheffler, “A Second Order Accurate Numerical Approximation for the Fractional Diffusion Equation,” Journal of Computational Physics, Vol. 213, No. 1, 2006, pp. 205-213. http://dx.doi.org/10.1016/j.jcp.2005.08.008
|
[11]
|
M. M. Meerschaert and C. Tadjeran, “Finite Difference Approximations for Fractional Advection-Dispersion Flow Equations,” Journal of Computational and Applied Mathematics, Vol. 172, No. 1, 2004, pp. 65-77. http://dx.doi.org/10.1016/j.cam.2004.01.033
|
[12]
|
L. Blank, “Numerical Treatment of Differential Equations of Fractional Order,” Numerical Analysis Report 287, Manchester Centre for Computational Mathematics, Manchester, 1996.
|
[13]
|
K. Diethelm and G. Walz, “Numerical Solution of Fractional Order Differential Equations by Extroplation,” Numerical Algorithms, Vol. 16, 1997, pp. 231-253. http://dx.doi.org/10.1023/A:1019147432240
|
[14]
|
K. Diethelm, “An Algorithm for the Numerical Solution of Differential Equations of Fractional Order,” Electronic Transactions on Numerical Analysis, Vol. 5, 1997, pp. 1-6.
|
[15]
|
N. Ford and A. Simpson, “The Numerical Solution of Fractional Differential Equations: Speed versus Accuracy,” Numerical Analysis Report 385, Manchester Centre for Computational Mathematics, Manchester, 2001.
|
[16]
|
K. Diethelm, N. Ford and A. Freed, “A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations,” Nonlinear Dynamics, Vol. 29, No. 1-4, 2002, pp. 3-22. http://dx.doi.org/10.1023/A:1016592219341
|
[17]
|
C.-M. Chen, F. Liu and K. Burrage, “Finite Difference Methods and a Fourier Analysis for the Fractional Reaction-Subdiffusion Equation,” Applied Mathematics and Computation, Vol. 198, No. 2, 2008, pp. 754-769. http://dx.doi.org/10.1016/j.amc.2007.09.020
|
[18]
|
B. Baeumer, M. Kovacs and M. M. Meerschaert, “Numerical Solutions for Fractional Reaction-Diffusion Equations,” Computers & Mathematics with Applications, Vol. 55, No. 10, 2008, pp. 2212-2226. http://dx.doi.org/10.1016/j.camwa.2007.11.012
|
[19]
|
S. Shen, F. Liu and V. Anh, “Numerical Approximations and Solution Techniques for the Space-Time Riesz-Caputo Fractional Advection-Diffusion Equation,” Numerical Algorithms, Vol. 56, No. 3, 2011, pp. 383-403. http://dx.doi.org/10.1007/s11075-010-9393-x
|
[20]
|
C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, “Spectral Methods. Fundamentals in Single Domains,” Springer-Verlag, Berlin, 2006.
|
[21]
|
D. Funaro and D. Gottlieb, “A New Method of Imposing Boundary Conditions in Pseudospectral Approximations of Hyperbolic Equations,” Mathematical and Computer, Vol. 51, No. 184, 1988, pp. 599-613. http://dx.doi.org/10.1090/S0025-5718-1988-0958637-X
|
[22]
|
G.-Q. Chen, Q. Du and E. Tadmor, “Spectral Viscosity Approximations to Multidimensional Scalar Conservation Laws,” Mathematical and Computer, Vol. 61, No. 204, 1993, pp. 629-643. http://dx.doi.org/10.1090/S0025-5718-1993-1185240-3
|
[23]
|
T. Y. Hou and R. Li, “Computing Nearly Singular Solutions Using Pseudo-Spectral Methods,” Journal of Computational Physics, Vol. 226, No. 1, 2007, pp. 379-397. http://dx.doi.org/10.1016/j.jcp.2007.04.014
|
[24]
|
S. Esmaeili and M. Shamsi, “A Pseudo-Spectral Scheme for the Approximate Solution of a Family of Fractional Differential Equations,” Communications in Nonlinear Science & Numerical Simulation, Vol. 16, No. 9, 2011, pp. 3646-3654. http://dx.doi.org/10.1016/j.cnsns.2010.12.008
|
[25]
|
C. Li, F. Zeng and F. Liu, “Spectral Approximations to the Fractional Integral and Derivative,” Fractional Calculus & Applied Analysis, Vol. 15, No. 3, 2012, pp. 383-406. http://dx.doi.org/10.2478/s13540-012-0028-x
|
[26]
|
J. Shen and T. Tang, “Spectral and High-Order Methods with Applications,” Science Press, Beijing, 2007.
|
[27]
|
A. Quarteroni and A. Valli, “Numerical Approximation of Partial Differential Equations,” Springer-Verlag, Berlin, 1997.
|