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Simpson’s 3/8 Rule By: Mufan Yang. What is Simpson’s 3/8 Rule Simpson’s 3/8 is very similar to the Simpson’s Method that we already learned in class.

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Presentation on theme: "Simpson’s 3/8 Rule By: Mufan Yang. What is Simpson’s 3/8 Rule Simpson’s 3/8 is very similar to the Simpson’s Method that we already learned in class."— Presentation transcript:

1 Simpson’s 3/8 Rule By: Mufan Yang

2 What is Simpson’s 3/8 Rule 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 called Simpson’s 1/3 Method) uses a second degree polynomial (quadratic)

3 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.

4 How do we get the formula: We begin by integrating the 3rd degree Polynomial p(t)=c 3 t 3 +c 2 t 2 +c 1 t+c 0.

5

6 h = (−)/N, where N is a positive multiple of 3 so another way to look at this is h = (−)/3, where n is the number of partitions being used.

7 Here we are using a single partition. xy ay 0 =f(a) a+hy 1 =f(a+h) a+2hy 2 =f(a+2h) a+3hy 3 =f(b) ab=a+3ha + h a + 2h

8 a+3h a+4h a+5hb = a+6h

9 Conclusion: 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.

10 Example:

11 Simpson’s 1/3 Rule VS Simpson’s 3/8 Rule Advantages: Can use an odd or even number of subintervals rather than just an even number of subintervals as used in the Simpson’s 1/3 Rule. Can converge to estimated integral values much quicker than Simpson’s 1/3 Rule Has the same order of accuracy as the Simpson’s 1/3 Rule when calculating the absolute error, but the Simpson’s 3/8 Rule is actually slightly more accurate. But the fraction used in this error will be smaller and then will provide a more accurate error. Disadvantages: This rule requires multiple of 3 segments only. When calculating the value by hand this rule is more complicated. 1/3 Rule: and

12 References Module for Simpson’s 3/8 Rule for Numerical Integration. (2012). Retrieved from Nguyen, Duc. Chapter 07.08: Simpson 3/8 Rule For Integration. University of South Florida. Wikipedia. Simpson’s Rule. Retrieved from


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