This post contains additional information related to the Numerical Methods Project posted last week, due March 23rd.

Submission guidelines. Your completed project will consist of three elements:

  1. A working numerical methods calculator using your choice of technology (spreadsheet, programming, mathematical software), as described in the previous post.
    HOW TO SUBMIT:

    • If your project is a spreadsheet, either share it with me (if it is in Google Docs or a similar cloud-based platform), or email the file to me as an attachment.
    • If your project is code, please submit it using an online coding site like ideone.com – once your code is working on the site, you can simply submit a link.  If you are using a programming language not supported by ideone.com, you can email the source code to me.
    • If your project uses mathematical software, either share it with me (if it is in MatLab Online or a similar cloud-based platform), or email the file to me as an attachment.
  2. Solutions to the following example using each of the three methods studied in class (Euler’s Method, Improved Euler’s Method, and Runge-Kutta), generated by your numerical methods calculator.  Submit using the same method as in part 1.

Project Example.  Given the differential equation dy/dx = \frac{xy}{x-y} and initial condition y(6)=0.8, approximate the value of y(7.1) using Euler’s Method, Improved Euler’s Method, and Runge-Kutta.

For each method, choose a step size that gives four correct digits following the decimal point.  How many steps are required to obtain this level of precision?

NOTE: The actual solution is y(7.1)=3.700936…

  1. Writing assignment.  Write one or two paragraphs (minimum 300 words) responding to the following.  Leave your response as a comment on this post.
    1. Describe your project and how it works.
    2. Describe the process of building your numerical methods calculator.  What kind of technology did you decide to use, and why? Did you encounter any unexpected challenges in completing this project?
    3. Why do we need numerical methods in addition to the other methods studied in the class?
    4. Why is this assignment included in the class (instead of just computing the various methods using a calculator)?
    5. Please include a link to your project (if it is online), or clearly state that you will be sending me the files by email (and don’t forget to do it!).