-
3
-
-
0040307478
-
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
-
J. Bouchaud and A. Georges, Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications, Phys. Rep., 195 (1990), pp. 127-293.
-
(1990)
Phys. Rep.
, vol.195
, pp. 127-293
-
-
Bouchaud, J.1
Georges, A.2
-
4
-
-
0002641421
-
The random walk's guide to anomalous diffusion: A fractional dynamics approach
-
R. Metzler and J. Klafter, The random walk's guide to anomalous diffusion: A fractional dynamics approach, Phys. Rep., 339 (2000), pp. 1-77.
-
(2000)
Phys. Rep.
, vol.339
, pp. 1-77
-
-
Metzler, R.1
Klafter, J.2
-
5
-
-
0001691616
-
Observations of anomalous diffusion and Lévy flights in a 2-dimensional rotating flow
-
T. H. Solomon, E. R. Weeks, and H. L. Swinney, Observations of anomalous diffusion and Lévy flights in a 2-dimensional rotating flow, Phys. Rev. Lett., 71 (1993), pp. 3975-3979.
-
(1993)
Phys. Rev. Lett.
, vol.71
, pp. 3975-3979
-
-
Solomon, T.H.1
Weeks, E.R.2
Swinney, H.L.3
-
6
-
-
0009481303
-
Fractional diffusion equation
-
W. Wyss, Fractional diffusion equation, J. Math. Phys., 27 (1986), pp. 2782-2785.
-
(1986)
J. Math. Phys.
, vol.27
, pp. 2782-2785
-
-
Wyss, W.1
-
7
-
-
0001553919
-
Fractional diffusion and wave equations
-
W. R. Schneider and W. Wyss, Fractional diffusion and wave equations, J. Math. Phys., 30 (1989), pp. 134-144.
-
(1989)
J. Math. Phys.
, vol.30
, pp. 134-144
-
-
Schneider, W.R.1
Wyss, W.2
-
8
-
-
30244460855
-
The fundamental solutions for the fractional diffusion-wave equation
-
DOI 10.1016/0893-9659(96)00089-4, PII S0893965996000894
-
F. Mainardi, The fundamental solutions for the fractional diffusion-wave equation, Appl. Math. Lett., 9 (1996), pp. 23-28. (Pubitemid 126365654)
-
(1996)
Applied Mathematics Letters
, vol.9
, Issue.6
, pp. 23-28
-
-
Mainardi, F.1
-
9
-
-
0036650850
-
Time fractional diffusion: A discrete random walk approach
-
DOI 10.1023/A:1016547232119, Fractional Order Calculus and Its Applications
-
R. Gorenflo, F. Mainardi, D. Moretti, and P. Paradisi, Time fractional diffusion: A discrete random walk approach, Nonlinear Dyn., 29 (2002), pp. 129-143. (Pubitemid 34945395)
-
(2002)
Nonlinear Dynamics
, vol.29
, Issue.1-4
, pp. 129-143
-
-
Gorenflo, R.1
Mainardi, F.2
Moretti, D.3
Paradisi, P.4
-
10
-
-
34047155650
-
Continuous-time random walk and parametric subordination in fractional diffusion
-
DOI 10.1016/j.chaos.2007.01.052, PII S0960077907000926
-
R. Gorenflo, F. Mainardi, and A. Vivoli, Continuous-time random walk and parametric subordination in fractional diffusion, Chaos Solitons Fractals, 34 (2007), pp. 87-103. (Pubitemid 46529249)
-
(2007)
Chaos, Solitons and Fractals
, vol.34
, Issue.1
, pp. 87-103
-
-
Gorenflo, R.1
Mainardi, F.2
Vivoli, A.3
-
11
-
-
0036650559
-
Solution for a fractional diffusion-wave equation defined in a bounded domain
-
DOI 10.1023/A:1016539022492, Fractional Order Calculus and Its Applications
-
O. P. Agrawal, Solution for a fractional diffusion-wave equation defined in a bounded domain, Nonlinear Dynam., 29 (2002), pp. 145-155. (Pubitemid 34945396)
-
(2002)
Nonlinear Dynamics
, vol.29
, Issue.1-4
, pp. 145-155
-
-
Agrawal, O.P.1
-
12
-
-
25444472344
-
An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations
-
DOI 10.1137/030602666
-
S. B. Yuste and L. Acedo, An explicit finite difference method and a new von Neumanntype stability analysis for fractional diffusion equations, SIAM J. Numer. Anal., 42 (2005), pp. 1862-1874. (Pubitemid 41634613)
-
(2005)
SIAM Journal on Numerical Analysis
, vol.42
, Issue.5
, pp. 1862-1874
-
-
Yuste, S.B.1
Acedo, L.2
-
13
-
-
33646128485
-
Weighted average finite difference methods for fractional diffusion equations
-
DOI 10.1016/j.jcp.2005.12.006, PII S0021999105005516
-
S. B. Yuste, Weighted average finite difference methods for fractional diffusion equations, J. Comput. Phys., 216 (2006), pp. 264-274. (Pubitemid 43632555)
-
(2006)
Journal of Computational Physics
, vol.216
, Issue.1
, pp. 264-274
-
-
Yuste, S.B.1
-
14
-
-
36149001420
-
A Fourier method for the fractional diffusion equation describing sub-diffusion
-
C. M. Chen, F. Liu, I. Turner, and V. Anh, A Fourier method for the fractional diffusion equation describing sub-diffusion, J. Comput. Phys., 227 (2007), pp. 886-897.
-
(2007)
J. Comput. Phys.
, vol.227
, pp. 886-897
-
-
Chen, C.M.1
Liu, F.2
Turner, I.3
Anh, V.4
-
15
-
-
17144427014
-
The accuracy and stability of an implicit solution method for the fractional diffusion equation
-
DOI 10.1016/j.jcp.2004.11.025, PII S0021999104004887
-
T. A. M. Langlands and B. I. Henry, The accuracy and stability of an implicit solution method for the fractional diffusion equation, J. Comput. Phys., 205 (2005), pp. 719-736. (Pubitemid 40518394)
-
(2005)
Journal of Computational Physics
, vol.205
, Issue.2
, pp. 719-736
-
-
Langlands, T.A.M.1
Henry, B.I.2
-
16
-
-
55549107511
-
New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation
-
P. Zhuang, F. Liu, V. Anh, and I. Turner, New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation, SIAM J. Numer. Anal., 46 (2008), pp. 1079-1095.
-
(2008)
SIAM J. Numer. Anal.
, vol.46
, pp. 1079-1095
-
-
Zhuang, P.1
Liu, F.2
Anh, V.3
Turner, I.4
-
17
-
-
30744474991
-
A fully discrete difference scheme for a diffusion-wave system
-
Z. Z. Sun and X. N. Wu, A fully discrete difference scheme for a diffusion-wave system, Appl. Numer. Math., 56 (2006), pp. 193-209.
-
(2006)
Appl. Numer. Math.
, vol.56
, pp. 193-209
-
-
Sun, Z.Z.1
Wu, X.N.2
-
18
-
-
33646398146
-
Convolution quadrature time discretization of fractional diffusion-wave equations
-
DOI 10.1090/S0025-5718-06-01788-1, PII S0025571806017881
-
E. Cuesta, C. Lubich, and C. Palencia, Convolution quadrature time discretization of fractional diffusion-wave equations, Math. Comp., 75 (2006), pp. 673-696. (Pubitemid 43681466)
-
(2006)
Mathematics of Computation
, vol.75
, Issue.254
, pp. 673-696
-
-
Cuesta, E.1
Lubich, C.2
Palencia, C.3
-
19
-
-
69049086472
-
Compact finite difference method for the fractional diffusion equation
-
M. Cui, Compact finite difference method for the fractional diffusion equation, J. Comput. Phys., 228 (2009), pp. 7792-7804.
-
(2009)
J. Comput. Phys.
, vol.228
, pp. 7792-7804
-
-
Cui, M.1
-
20
-
-
77952888765
-
A compact difference scheme for the fractional diffusionwave equation
-
R. Du, W. R. Cao, and Z. Z. Sun, A compact difference scheme for the fractional diffusionwave equation, Appl. Math. Model., 34 (2010), pp. 2998-3007.
-
(2010)
Appl. Math. Model.
, vol.34
, pp. 2998-3007
-
-
Du, R.1
Cao, W.R.2
Sun, Z.Z.3
-
21
-
-
77955704784
-
Numerical schemes with high spatial accuracy for a variable-order anomalous subdiffusion equation
-
C. M. Chen, F. Liu, V. Anh, and I. Turner, Numerical schemes with high spatial accuracy for a variable-order anomalous subdiffusion equation, SIAM J. Sci. Comput., 32 (2010), pp. 1740-1760.
-
(2010)
SIAM J. Sci. Comput.
, vol.32
, pp. 1740-1760
-
-
Chen, C.M.1
Liu, F.2
Anh, V.3
Turner, I.4
-
22
-
-
78649334165
-
A compact difference scheme for the fractional sub-diffusion equations
-
G. H. Gao and Z. Z. Sun, A compact difference scheme for the fractional sub-diffusion equations, J. Comput. Phys., 230 (2011), pp. 586-595.
-
(2011)
J. Comput. Phys.
, vol.230
, pp. 586-595
-
-
Gao, G.H.1
Sun, Z.Z.2
-
23
-
-
84907893973
-
Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term
-
P. Zhuang, F. Liu, V. Anh, and I. Turner, Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term, SIAM J. Numer. Anal., 47 (2009), pp. 1760-1781.
-
(2009)
SIAM J. Numer. Anal.
, vol.47
, pp. 1760-1781
-
-
Zhuang, P.1
Liu, F.2
Anh, V.3
Turner, I.4
-
24
-
-
79956124918
-
A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
-
X. Zhao and Z. Z. Sun, A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions, J. Comput. Phys., 230 (2011), pp. 6061-6074.
-
(2011)
J. Comput. Phys.
, vol.230
, pp. 6061-6074
-
-
Zhao, X.1
Sun, Z.Z.2
-
25
-
-
84862921732
-
Error estimates of crank-nicolson-type difference schemes for the subdiffusion equation
-
Y. N. Zhang, Z. Z. Sun, and H. W. Wu, Error estimates of Crank-Nicolson-type difference schemes for the subdiffusion equation, SIAM J. Numer. Anal., 49 (2011), pp. 2302-2322.
-
(2011)
SIAM J. Numer. Anal.
, vol.49
, pp. 2302-2322
-
-
Zhang, Y.N.1
Sun, Z.Z.2
Wu, H.W.3
-
26
-
-
77951184169
-
An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation
-
Y. Gu, P. Zhuang, and F. Liu, An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation, CMES Comput. Model. Eng. Sci., 56 (2010), pp. 303-333.
-
(2010)
CMES Comput. Model. Eng. Sci.
, vol.56
, pp. 303-333
-
-
Gu, Y.1
Zhuang, P.2
Liu, F.3
-
27
-
-
34547548712
-
Finite difference/spectral approximations for the time-fractional diffusion equation
-
Y. Lin and C. Xu, Finite difference/spectral approximations for the time-fractional diffusion equation, J. Comput. Phys., 225 (2007), pp. 1533-1552.
-
(2007)
J. Comput. Phys.
, vol.225
, pp. 1533-1552
-
-
Lin, Y.1
Xu, C.2
-
28
-
-
77958536189
-
A space-time spectral method for the time fractional diffusion equation
-
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.
-
(2009)
SIAM J. Numer. Anal.
, vol.47
, pp. 2108-2131
-
-
Li, X.1
Xu, C.2
-
29
-
-
79955669422
-
Finite difference/spectral approximations for the fractional cable equation
-
Y. Lin, X. Li, and C. Xu, Finite difference/spectral approximations for the fractional cable equation, Math. Comp., 80 (2011), pp. 1369-1396.
-
(2011)
Math. Comp.
, vol.80
, pp. 1369-1396
-
-
Lin, Y.1
Li, X.2
Xu, C.3
-
30
-
-
59349113701
-
Finite element method for the the space and time fractional Fokker-Planck equation
-
W. Deng, Finite element method for the the space and time fractional Fokker-Planck equation, SIAM J. Numer. Anal., 47 (2008), pp. 204-226.
-
(2008)
SIAM J. Numer. Anal.
, vol.47
, pp. 204-226
-
-
Deng, W.1
-
31
-
-
77950690888
-
Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation
-
C. M. Chen, F. Liu, I. Turner, and V. Anh, Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation, Numer. Algorithms, 54 (2010), pp. 1-21.
-
(2010)
Numer. Algorithms
, vol.54
, pp. 1-21
-
-
Chen, C.M.1
Liu, F.2
Turner, I.3
Anh, V.4
-
32
-
-
80053633596
-
Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
-
Y. N. Zhang and Z. Z. Sun, Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation, J. Comput. Phys., 230 (2011), pp. 8713-8728.
-
(2011)
J. Comput. Phys.
, vol.230
, pp. 8713-8728
-
-
Zhang, Y.N.1
Sun, Z.Z.2
-
33
-
-
77954142858
-
Numerical simulations of 2D fractional subdiffusion problems
-
H. Brunner, L. Ling, and M. Yamamoto, Numerical simulations of 2D fractional subdiffusion problems, J. Comput. Phys., 229 (2010), pp. 6613-6622.
-
(2010)
J. Comput. Phys.
, vol.229
, pp. 6613-6622
-
-
Brunner, H.1
Ling, L.2
Yamamoto, M.3
-
34
-
-
80053638646
-
Finite difference approximation for two-dimensional time fractional diffusion equation
-
P. Zhuang and F. Liu, Finite difference approximation for two-dimensional time fractional diffusion equation, J. Algorithm Computat. Tech., 1 (2007), pp. 1-15.
-
(2007)
J. Algorithm Computat. Tech.
, vol.1
, pp. 1-15
-
-
Zhuang, P.1
Liu, F.2
-
35
-
-
84858987832
-
Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation
-
C. Chen, F. Liu, V. Anh, and I. Turner, Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation, Math. Comp., 81 (2011), pp. 345-366.
-
(2011)
Math. Comp.
, vol.81
, pp. 345-366
-
-
Chen, C.1
Liu, F.2
Anh, V.3
Turner, I.4
-
36
-
-
63949084174
-
A numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection-diffusion equation
-
C. Chen and F. Liu, A numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection-diffusion equation, J. Appl. Math. Comput., 30 (2009), pp. 219-236.
-
(2009)
J. Appl. Math. Comput.
, vol.30
, pp. 219-236
-
-
Chen, C.1
Liu, F.2
-
37
-
-
84865609778
-
Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions
-
Q. Yang, T. Moroney, K. Burrage, I. Turner, and F. Liu, Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions, ANZIAM J. Electron. Suppl., 52 (2010), pp. C395-C409.
-
(2010)
ANZIAM J. Electron. Suppl.
, vol.52
-
-
Yang, Q.1
Moroney, T.2
Burrage, K.3
Turner, I.4
Liu, F.5
-
38
-
-
79960431454
-
Novel numerical methods for solving the timespace fractional diffusion equation in two dimensions
-
Q. Yang, I. Turner, F. Liu, and M. Ilić, Novel numerical methods for solving the timespace fractional diffusion equation in two dimensions, SIAM J. Sci. Comput., 33 (2011), pp. 1159-1180.
-
(2011)
SIAM J. Sci. Comput.
, vol.33
, pp. 1159-1180
-
-
Yang, Q.1
Turner, I.2
Liu, F.3
Ilić, M.4
-
39
-
-
84856227286
-
Modified alternating direction methods for solving a two-dimensional noncontinuous seepage flow with fractional derivatives in uniform media
-
Q. Liu and F. Liu, Modified alternating direction methods for solving a two-dimensional noncontinuous seepage flow with fractional derivatives in uniform media, Math. Numer. Sin., 31 (2009), pp. 179-194.
-
(2009)
Math. Numer. Sin.
, vol.31
, pp. 179-194
-
-
Liu, Q.1
Liu, F.2
-
40
-
-
63649135242
-
Numerical simulation for the three-dimensional seepage flow with fractional derivatives in porous media
-
Q. Liu, F. Liu, I. Turner, and V. Anh, Numerical simulation for the three-dimensional seepage flow with fractional derivatives in porous media, IMA J. Appl. Math., 74 (2009), pp. 201-229.
-
(2009)
IMA J. Appl. Math.
, vol.74
, pp. 201-229
-
-
Liu, Q.1
Liu, F.2
Turner, I.3
Anh, V.4
-
41
-
-
49249094092
-
ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation
-
S. Chen and F. Liu, ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation, J. Appl. Math. Comput., 26 (2008), pp. 295-311.
-
(2008)
J. Appl. Math. Comput.
, vol.26
, pp. 295-311
-
-
Chen, S.1
Liu, F.2
-
42
-
-
0025383598
-
Difference scheme for a nonlinear partial integrodifferential equation
-
J. C. López-Marcos, A difference scheme for a nonlinear partial integrodifferential equation, SIAM J. Numer. Anal., 27 (1990), pp. 20-31. (Pubitemid 20669394)
-
(1990)
SIAM Journal on Numerical Analysis
, vol.27
, Issue.1
, pp. 20-31
-
-
Lopez-Marcos, J.C.1
-
43
-
-
0012661804
-
A finite difference scheme for partial integro-differential equations with a weakly singular kernel
-
T. Tang, A finite difference scheme for partial integro-differential equations with a weakly singular kernel, Appl. Numer. Math., 11 (1993), pp. 309-319.
-
(1993)
Appl. Numer. Math.
, vol.11
, pp. 309-319
-
-
Tang, T.1
|