1
9.13 In the standard Simpson’s 1/3 method (Eq. (9.16)), the points used for the integration are the
endpoints of the domain, a and b, and the middle point . Derive a new formula for Simpson’s 1/3
method in which the points used for the integration are , , and .
This can be further simplified to yield:
or,
ab+()2⁄
xa=
xb=
xab+()3⁄=
6
ba–()bx
2
–()
x2a–()bx
2
–()
–2b3a33ab2
Ifa()ba–()
fx
2
()fa()–[]
2x2a–()
-------------------------------- ba–()
2
+=
1
6
---fb() fa()–
ba–()bx
2
–()
------------------------------------fx
2
()fa()–
x2a–()bx
2
–()
--------------------------------------
–b32ab2
–a2b+{}+
2