Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number.

At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

1.
M.
Basu
and
D. P.
Acharya
,
Journal of Applied Mathematics and Computing
10
(
1-2
),
131
143
(
2002
).
2.
A. A. A.
Kilbas
,
H. M.
Srivastava
and
J. J.
Trujillo
,
Theory and applications of fractional differential equations
. (
Elsevier Science Limited
,
2006
).
3.
I.
Podlubny
,
MATHEMATICS IN SCIENCE AND ENGI-NEERING
198
(
1999
).
4.
Q.
Huang
,
G.
Huang
and
H.
Zhan
,
Advances in Water Resources
31
(
12
),
1578
1589
(
2008
).
5.
A.
Kadem
,
Y.
Luchko
and
D.
Baleanu
,
Reports on Mathematical Physics
66
(
1
),
103
115
(
2010
).
6.
Y.
Zhang
,
Applied Mathematics and Computation
215
(
2
),
524
529
(
2009
).
7.
W.
Hackbusch
,
Iterative solution of large sparse systems of equations
. (
Springer
,
1994
).
8.
D. M.
Young
,
Journal of Approximation Theory
5
(
2
),
137
148
(
1972
).
9.
Y.
Saad
,
Iterative methods for sparse linear systems
. (
Siam
,
2003
).
10.
D.
Evans
and
W.
Yousif
,
International journal of computer mathematics
18
(
3-4
),
323
340
(
1986
).
11.
A. R.
Abdullah
,
International Journal of Computer Mathematics
38
(
1-2
),
61
70
(
1991
).
12.
M.
Othman
and
A.
Abdullah
,
International Journal of Computer Mathematics
76
(
2
),
203
217
(
2000
).
13.
N. H. M.
Ali
and
N. K.
Fu
, presented at
the Proceedings of the 12th WSEAS International Conference on Applied Mathematics
,
2007
(unpublished).
14.
N. H. M.
Ali
and
L. M.
Kew
,
Journal of Computational Physics
231
(
20
),
6953
6968
(
2012
).
15.
N. H. M.
Ali
and
T. W.
Ping
.
16.
T. K.
Bee
,
N. H. M.
Ali
and
C.-H.
Lai
, presented at
the Proceedings of the World Congress on Engineering
,
2010
(unpublished).
17.
K. L.
Ming
and
N. H. M.
Ali
,
ijm
1
(
1
),
2
(
2010
).
18.
Y.-n.
Zhang
and
Z.-z.
Sun
,
Journal of Computational Physics
230
(
24
),
8713
8728
(
2011
).
19.
I.
Karatay
,
N.
Kale
and
S. R.
Bayramoglu
,
Fractional Calculus and Applied Analysis
16
(
4
),
892
910
(
2013
).
20.
M.
Cui
,
Numerical Algorithms
62
(
3
),
383
409
(
2013
).
This content is only available via PDF.