Other numerical methods 277
α 3 3
1
2
6 2 2
2
,
(
)
= +
+
+
u u
t
x
S e
∆
∆
(9.95)
α 3 4 6
, = g
t
x
∆
∆
(9.96)
α
λ
λ
ζ
λ
4 1
1
6
1
2
4
24
4
4
,
(
)
= − +
+
+
−

 

  +
−

 

h
h
S x
x
x
o ∆
∆
∆
  






ζ 2
∆
∆
t
x
(9.97)
α 4 2
1
2
3 2
2
,
(
)
= −
+
u
u
t
x
∆
∆
(9.98)
α
λ
λ
ζ
λ
ζ
4 3
1
2
6
4
2
4
,
(
)
(
)
=
+
+
+
+

 

  +
+





h h
S x
x
x
o ∆
∆
∆
 
∆
∆
t
x
(9.99)
α 4 4
1
2
2 3
2
,
(
)
=
+
+






u
u
t
x
∆
∆
(9.100)
c
u u
u u u u
g
t
x
1
1
2
1
2
1 2
2
2
1
2
3 2
2
3
1
2
=
+
+
−
− +
−
 
 
−
(
)
(
)
ζ ζ
∆
∆
( (
)
2 1
2
u u S e
+
(9.101)
c
h
h
S x u
h
h
S x u
o
o
2
1
3
1
2
3
1
4
=
−
+





 −
+
+






(
)
(
)
λ
λ
∆
∆
2 2






∆
∆
t
x
+
−

 

 
− +

 

 
+
− +
4
3
8
1
1
8
2
1
1 1
1 2
2 1
λ
ζ
λ
ζ
ζ
∆
∆
x u
x u
u
(
)
8 8
2 2
λ
ζ
∆
∆
∆
x u
t
x

 

 






+3(2ζ 1 + ζ 2 )
(9.102)