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Unformatted text preview: ASE 211 Homework 11
Due: in class, Wednesday, Apr. 23rd.
1. Write a matlab m-ﬁle which implements the Simpson’s rule. Test
your code by showing that it computes the following integral exactly:
2 (x3 + 3x2 − 2x + 3)dx 0 2. Next, generalize your m-ﬁle to the composite Simpson’s rule and test
it on the integral
1 6x5 dx = 1, 0 and show that as you double n = 2, 4, 8, the error goes to zero like h4 (the
error should go down approximately by a factor of 16 with each doubling).
Remark This extra order of convergence comes from the fact that Simpson’s rule, although designed to integrate all quadratics exactly, happens to
also integrate all cubics exactly. As a result, the single interval rule attains
O(h5 ), and the multiple interval rule attains order O(h4 ). Please make this
correction in your notes.
3. Apply the code written above to the function in problem 17.2 in the
book. Use at least n = 10. ...
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This note was uploaded on 09/18/2011 for the course ASE 211 taught by Professor N/a during the Spring '08 term at University of Texas.
- Spring '08