15.6. Error Analysis

Try these first

1. 1.

   What is Local Truncation Error?

   Hint

   Think about errors in a single computation step.

2. 2.

   What is the order of the Local Truncation Error for a 2-step Adams–Bashforth method?

   Hint

   Recall how the order is related to the number of steps.

3. 3.

   What is Local Truncation Error for k-step methods?

   • O(h^k)
   • O(h^(k+1))
   • O(h^(k-1))

   Hint

   Focus on the error per step.

4. 4.

   True or False: Global Error accumulates throughout the numerical method.

   • True
   • False

   Hint

   Think about how errors build up.

5. 5.

   Calculate the Local Truncation Error for a 4-step Adams-Bashforth method with a given step size.

   Hint

   Examine the general form for k-step errors.

6. 6.

   Explain how increasing the step size would impact both Local and Global Error based on theoretical concepts.

   Hint

   Compare with the error equations we've learned.