17.1.2. Local Truncation Error (LTE)

Try these first

1. 1.

   Define Local Truncation Error.

   Hint

   What happens in one step that leads to error?

2. 2.

   What is the LTE for Euler’s Method?

   Hint

   How does the step size affect the error in Euler's method?

3. 3.

   What is Local Truncation Error (LTE)?

   • The error in a single integration step
   • The cumulative error
   • The total error in a method

   Hint

   Think about what happens in one step of approximation.

4. 4.

   Higher-order methods generally lead to what outcome regarding error?

   • True
   • False

   Hint

   Focus on how method order impacts convergence.

5. 5.

   If the true value of a function at x=1 is 4 and using Euler's method, you find it to be 3.5 with a step size of 0.2, calculate the Local Truncation Error.

   Hint

   Apply the formula: LTE = true value - numerical value.

6. 6.

   How would you adjust a numerical method to improve accuracy if the Local Truncation Error is significantly high? Discuss two strategies.

   Hint

   Think about how step size impacts accuracy or strategy changes in method selection.