Math 306 - Lab 1
Euler Method Error Analysis

This lab is due Thursday, February 5, in class. No late reports will be accepted. Beware of problems printing or long waits for printouts.
You are expected to turn in:

Your goal in this lab is to look at how the error varies with the step size Delta t when using Euler's method to approximate the solution to a differential equation.

1. You will use the initial value problem

dy/dt= y+A, y(0) = y0 =B,

where A is the last non-zero digit in your student ID and B is the second last nonzero digit. For example, if your student ID is 12345678, then A = 8 and B=7 If your ID is 80070600, then A=6 and B=7.
Solve the ODE analytically. You may use dsolve to check your answer, but you need to show the work for your actual solution.
Get the value of y(1) by using the Maple evalf command.

2. Now use Maple code for Euler's method with step size Delta t= 0.1 to approximate y(1). Recall that there is Maple code for Euler's method at the link for section 1.4 on the Math 306 resources page. You don't need to make a list or plot your approximation, just compute and display y(1). Then compute the error for Delta t= 0.1.

3. Repeat with Delta t= 0.05, again displaying y(1) and the error.

4. Repeat with Delta t= 0.025, again displaying y(1) and the error.

5. What happens to the error as the step size is halved?

6. Does the same thing happen when the step size is scaled by other factors, e.g., reduced by a 1/10? Do a couple more experiments to answer this question.