Civil Engineering Reference
In-Depth Information
f(x)
x
n
(x)
x
n+3
x
n+1
x
n+2
Figure 1.7.
Newton-Raphson method or Newton's tangent.
f(x)
x
n+1
x
n+3
x
n+4
(x)
x
n
x
n+2
Figure 1.8.
Newton-Raphson method or Newton's tangent.
The derivative of the function must be obtained to find the slope at any
given value.
()
=− +
3
2
fx x
84
.
x
20 16
.
x
−
13 824
.
′
()
=− +
fx x
3 68 20 16
2
.
x
.
Beginning with
x
n
= 1.25, use Equation 1.2 to determine the next value.
(
)
=
(
)
+
2
(
)
−
3
f
f
125125 84125 016125
.
.
−
.
.
.
.
13 824
.
=
0 2041
.
′
(
)
(
)
+
125
.
=
3125
(. )
2
−
16 8125
.
.
20 16
.
=
3 8475
.
=−
()
fx
fx
0 2041
3 8475
.
.
n
x
x
′
()
=
125
.
−
=
1 1969
.
n
+
1
n
n
