Table 1:
The operations for generalized differential transform method.
Original function
Transformed function
𝑓
(
𝑛
,
𝑡
)
=
𝑔
(
𝑛
,
𝑡
)
+
ℎ
(
𝑛
,
𝑡
)
𝐹
(
𝑛
,
𝑘
)
=
𝐺
(
𝑛
,
𝑘
)
+
𝐻
(
𝑛
,
𝑘
)
𝑓
(
𝑛
,
𝑡
)
=
𝛼
𝑔
(
𝑛
,
𝑡
)
𝐹
(
𝑛
,
𝑘
)
=
𝛼
𝐺
(
𝑛
,
𝑘
)
𝑓
(
𝑛
,
𝑡
)
=
𝜕
𝑔
(
𝑛
,
𝑡
)
/
𝜕
𝑡
𝐹
(
𝑛
,
𝑘
)
=
(
𝑘
+
1
)
𝐺
(
𝑛
,
𝑘
+
1
)
𝑓
(
𝑛
,
𝑡
)
=
𝑔
(
𝑛
,
𝑡
)
ℎ
(
𝑛
,
𝑡
)
∑
𝐹
(
𝑛
,
𝑘
)
=
𝑘
𝑟
=
0
𝐺
(
𝑛
,
𝑟
)
𝐻
(
𝑛
,
𝑘
−
𝑟
)
𝑓
(
𝑛
,
𝑡
)
=
𝜕
𝑚
𝑔
(
𝑛
,
𝑡
)
/
𝜕
𝑡
𝑚
𝐹
(
𝑛
,
𝑘
)
=
(
𝑘
+
𝑚
)
𝐺
(
𝑛
,
𝑘
+
𝑚
)
𝑓
(
𝑛
,
𝑡
)
=
𝑔
(
𝑛
+
𝑠
,
𝑡
)
𝐹
(
𝑛
,
𝑘
)
=
𝐺
(
𝑛
+
𝑠
,
𝑘
)