9.5. Error in Euler’s Method

Try these first

1. 1.

   What is Local Truncation Error?

   Hint

   Think about the error in one calculation step.

2. 2.

   How does Global Truncation Error differ from Local Truncation Error?

   Hint

   Consider the difference in how errors accumulate.

3. 3.

   What does Local Truncation Error depend on?

   • h
   • h²
   • h³

   Hint

   Remember the relationship between LTE and step size.

4. 4.

   True or False: Global Truncation Error adds up errors over multiple steps.

   • True
   • False

   Hint

   Think about how errors might accumulate in a series.

5. 5.

   Suppose you have an ODE to solve where the step sizes are h = 0.1, h = 0.05, and h = 0.01. Compare the expected Local Truncation and Global Truncation Errors for these step sizes.

   Hint

   Think about how both types of errors relate to h squared and h.

6. 6.

   Design a numerical experiment using different step sizes for Euler’s Method on the same ODE, tracking how errors differ in your results at predetermined points.

   Hint

   Conduct the experiment focusing on both types of errors, ensuring clarity in recording outcomes.