17.1.1.2.1. Local Truncation Error (LTE)

Try these first

1. 1.

   Define Local Truncation Error (LTE).

   Hint

   Think about steps and how we compare exact with computed values.

2. 2.

   What is the order of LTE for Euler's method?

   Hint

   Recall the basic notation for order of accuracy.

3. 3.

   What does Local Truncation Error (LTE) represent?

   • Error over all steps
   • Error in a single step
   • Exact solution

   Hint

   Focus on the definition of LTE provided earlier.

4. 4.

   True or False: The order of a method increases with the step size.

   • True
   • False

   Hint

   Think about the relationship between error and step size.

5. 5.

   A differential equation has an exact solution. If you apply Euler's method with a step size of h and find an LTE of O(h^2), how would changing the step size impact the LTE?

   Hint

   Reflect on how 'h' relates to the error.

6. 6.

   You have options between Euler's method and a fourth-order Runge-Kutta method. Explain a scenario when you would choose one over the other based on LTE.

   Hint

   Consider the balance between computation time and required accuracy.