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Simpson 3/8 Rule for Integration . After reading this chapter, you should be able to . 1. derive the formula for Simpson’s 3/8 rule of integration, 2. use Simpson’s 3/8 rule it to solve integrals, 3. develop the formula for multiple-segment Simpson’s 3/8 rule of integration, 4.
1 (a) Numerically approximate the integral by using Simpson's 3/8 rule with m = 1, 2, 4. 1 (b) Find the analytic value of the integral (i.e. find the "true value"). 1 (c) Find the error for the Simpson' 3/8 rule approximations.
Figure 2: Illustration of (a) Simpson’s 1/3 rule, and (b) Simpson’s 3/8 rule Simpson’s 1 = 3 rule: Given function values at 3 points as ( x 0 ;f ( x 0 )), ( x 1 ;f ( x 1 )), and ( x 2 ;f ( x 2 )), we
Simpson’s Rule is based on the fact that given any three points, you can find the equation of a quadratic through those points. For example, let’s say you had points (3, 12), (1, 5), and (5, 9). Starting with (3, 12) and using y = ax2 + bx + c, you could write: x y. 12 = a(3)2 + b(3) + c.
Simpson’s 3/8th Rule. Similar to Simpson’s 1/3rd rule, if we take a third order polynomial we can derive the 3/8th rule as follows.
Aim: To evaluate a definite integral by Simpson’s 3/8 Rule Algorithm: 1. Given a function f(x): 2. (Get user inputs) Input a,b=endpoints of interval n=number of intervals(Even) (Do the integration) 3. Set h= (b-a)/n. 4. Set sum=0. 5. Begin For i= 1 to n -1 Set x =a + h*i. If i%3=0 Then Set sum=sum+2*f(x) Else Set sum=sum+3*f(x) End For 6.
However, in this problem we can combine the methods by appropriately dividing the interval: 1. We’ll use Simpson’s–1/3 rule on interval [1:0; 1:4] (4 subintervals is divisible by 2), and. 2. we’ll use Simpson’s–3/8 rule on interval [1:4; 1:7] (3 subintervals is divisible by 3).
