Simpson’s 3/8 Rule. By: Mufan Yang. What is Simpson’s 3/8 Rule.
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Simpson’s 3/8 is very similar to the Simpson’s Method that we already learned in class. The different is Simpson’s 3/8 method uses a third degree polynomial (cubic) to estimate the curve you are trying to find the integral of while Simpson’s Method (also calledSimpson’s 1/3 Method) uses a second degree polynomial (quadratic)
To get the estimate for an integral in this case, we will write out the 3rd degree polynomial using the general equation below and then integrate it.
We begin by integrating the 3rd degree
h = (𝑏−𝑎)/N , where Nis a positive multiple of 3 so another way to look at this is h = (𝑏−𝑎)/3𝑛 , where n is the number of partitions being used.
1 Partition =
a + h
a + 2h
() + ()
b = a+6h
So we can see that the equation for the Simpson’s 3/8 Rule is:
Each of the function values will be multiplied by 3 or 2 except for the first and the last. The number of subinterval points will need to be multiples of 3’s.
m = 1: h = 1:
m = 2: h =
m = 4: h =
= * 216 =20.25
Module for Simpson’s 3/8 Rule for Numerical Integration. (2012). Retrieved from http://math.fullerton.edu/mathews/n2003/Simpson38RuleMod.html.
Nguyen, Duc. Chapter 07.08: Simpson 3/8 Rule For Integration. University of South Florida. http://numbericalmethods.eng.usf.edu.
Wikipedia. Simpson’s Rule. Retrieved from http://en.wikipedia.org/wiki/Simpson%27s_rule.