MA/CS 371 - Lab 5
More Numerical Integration - The Composite Trapezoid Rule (CTR)
Versus The Composite Simpson's Rule (CSR)
Section 1: Introduction
In this lab you will:
- Write a practical implementation of the CSR
- Compare the convergence behavior of the CSR and the CTR.
If you have not already done so, create a directory for this lab and
copy the lab 5 files into it. If you start off in your home directory you
can do the following:
cp ~cs371/lab5/* .
and (as always) don't forget to type that last period.
Section 2: Topics for Lecture
Today in lecture I'm going to discuss the flops command which
is used to count the number of "floating-point operations" that MATLAB
performs. Comparing the "flops count" of two different algorithms is
one way of determining which is more efficient.
Section 3: Today's Function
Today's special guest function is one with some flat spots and some
f(x) = sin(e ) - e
This week we are going to estimate the integral of f(x) from -10 to 3
with the Composite Simpson's Rule and compare the results to the
Composite Trapezoid Rule.
First off, I recommend that you plot f(x) on the interval [-10,3] just
to see what it's doing. Make sure to use enough points that you can
see how the function wiggles around towards the upper end of the
Section 4: Implementing the Composite Trapezoid Rule
The trap.m file given to you for this lab is the one that I
wrote for the previous lab assignment. For this lab, you should
modify trap.m in the following ways:
- Approximate func(x) instead of 1-sin(x).
- Integrate from -10 to 3 instead of 0 to pi/2.
- Add another column to your table which shows how many
flops are required for each number of partitions.
Section 5: Implementing the Composite Simpson's Rule
Using your trap.m function as a template, make a new file
simpson.m which will approximate the integral with the CSR.
(Note: Problem 5.4.1 in the book contains the formula for the CSR.)
Use the same number of intervals as in trap.m and format
your output the same way.
Recall that the CSR requires an even number of intervals
(or an odd number of evaluation points.) You will need to change
the vector q in simpson.m to accommodate this.
Section 6: Submitting Your Work
When you are ready, run
to submit your simpson.m and trap.m files.