Civil Engineering Reference
In-Depth Information
(
)
+−
2
(
)
+
yaxbxc
y
=−
∆
∆
i
=
=
c
i
+
1
y
f xaxbxc
() () ()
=
∆
2
+
∆
+
i
+
2
Solving the three equations with three unknowns we obtain the following:
=
− +
()
=
−+
()
y
2
2
y
y
a
i
i
+
1
i
+
2
2
∆
x
yy
x
b
i
i
+
2
2
∆
cy
=
i
+
1
Substituting the expressions for
a
and
c
into Equation 3.4, the following
is achieved:
∆
3
x
(
)
A
=
y
+
4
y
+
y
i
i
+
1
i
+
2
If we apply this to
n
even numbered strips, the following occurs:
∆
x
(
)
A
=
y
+
4
y
+
y
1
2
3
3
∆
x
(
)
A
=
y
+
4
y
+
y
3
4
5
3
∆
x
(
)
A
=
y
+
4
y
+
y
5
6
7
3
∆
x
(
)
A
=
y
n
+
4
yy
n
+
−
1
n
+1
3
In general form, this is the following:
∆
3
x
n
n
−
1
∑∑
A
=
y
+
4
y
+
2
yy
+
1
i
i
n
+
1
i
=
246
,,
i
=
3 57
,,
If we performed the error truncation to obtain Romberg's integration, the
following occurs:
n
I
16
16
−
−
I
I
≅
h
2
h
1
n
1
