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ME 2016 Sections
Fall Semester 2007
Computing Techniques 3-0-3
Homework Assignment 6
Numerical Integration
Due: Friday, October 26, 2006 on the hour before class
IMPORTANT NOTE ON THE USE OF T-SQUARE
We all experienced significant problems with t-square the last two times assignments were due.
The support staff has identified that the problems originated with the tool “Assignments Auto-
Submission”. As a result, they have disabled the auto-submission feature. It will therefore be
your responsibility to submit. So, as previously, you can upload your zip-file using the save as
draft, but you will have to go back and click the final “Submit” button otherwise your assignment
will not be submitted. Remember, though, once you hit the “Submit” button, you can not go back
and upload an updated version. Because of the large number of students in ME2016, we cannot
accept revised versions after you have submitted.
Description and Outcomes
In this assignment, you will implement and test two numerical integration algorithms:
Trapezoidal and Simpson 1/3 integration. After implementing the two integration algorithms you
will compare their performance to the built-in Matlab function quad().
The learning objectives of this assignment are:
• to increase your understanding of numerical integration methods
• to learn about convergence rates and round-off errors
• to learn how to use numerical integration algorithms for solving engineering problems
• to learn how to create numerically efficient programs in Matlab
• to learn how to compare and interpret the performance of different numerical integration
algorithms
Background
In this assignment, the focus is on the implementation of several numerical integration
methods. The goal is to implement these algorithms efficiently in Matlab and to compare their
performance – that is: How does the absolute error change as a function of the number of
segments? You need to implement the Trapezoidal and Simpson 1/3 integration methods in such
a way that they are both fast and flexible to use. Program execution speed is crucial in this
assignment because we will be using the algorithms many times and for different numbers of
segments (up to 106 segments for a single integral).
Tasks
Task 1: Create the functions trapezoidal_integration_XYZ and simpson_integration_XYZ
(where XYZ are your initials)
To make it easier to perform the integration for different numbers of segments, start by
implementing the trapezoidal and Simpson 1/3 integration rules as separate functions. Each
function should have the following inputs and outputs:
Inputs:
1) a function handle, fhandle
2) the lower integration bound, a
3) the upper integration bound, b
4) the number of segments, n
