20
+
k1
2
+
k1
2
?
?
2
1
Penyelesaian:
k1 =
hf
(t
r
,
y
r
)
?
k
2
=
hf
?
t
r
?
+
1
h, y
2
r
1
?
?
?
k3 =
hf
(t
r
+
h, y
r
-
k1
+
2k
2
)
y
r
+1
= y
r
+
1
(k
6
1
+
4k
2
+
k3
)
t
0
=
0
?
y
0
=
4
t1 = 0.5 ? y1 = ?
k1 =
hf1
(t
0
,
y
0
,
z
0
) = 0.5{(0.5)(0.4)}
=
-1
?
k
2
=
hf1
?
t
0
?
+
1
h, y
2
0
+
1
k
,
z
2
1
0
1
?
?
?
k
2
=
(0.5)
f1
(0.25,3.5,5.5)
=
(0.5){(- 0.5)(3.5)}
=
-0.875
k3 =
hf1
(t
0
+
h, y
0
-
k1
+
2k
2
,
z
0
-
k1
+
2k
2
)
k3 =
(0.5)
f1
(0.5,3.25,6.815)
=
(0.5){(- 0.5)(3.25)}
=
-0.8125
sehingga
y1 = y
(0.5)
= y
0
+
1
(k
6
1
+
4k
2
+
k3
)
y
=
4
+
1
{- 1 + 4(- 0.875)
+
(- 0.8125)}
1
6
y1 = 3.114583
t
0
=
0
?
z
0
=
6
t1 = 0.5 ?
z1 = ?
k1 =
hf
2
(t
0
,
y
0
,
z
0
)
= 0.5
{4 - (0.3)(6)
-
(0.1)(4)}
=
0.9
k =
hf
?
t
+
1
h, y
+
1
k
,
z
+
1
k
?
2
2
0
?
0
2
1
0
2
?
k
2
=
(0.5)
f
2
(0.25,4.45,6.45)
 |