17..1.3. Global Truncation Error (GTE)

Try these first

1. 1.

   Define Global Truncation Error.

   Hint

   Think about how errors accumulate in numerical methods.

2. 2.

   What does the order of a method indicate?

   Hint

   Consider the relationship between step size and accuracy.

3. 3.

   What does Global Truncation Error (GTE) refer to?

   • Accumulated error over all steps
   • Error at one step
   • Error due to rounding

   Hint

   It involves the total action of many steps.

4. 4.

   True or False: Higher order methods always lead to less error.

   • True
   • False

   Hint

   Consider the balance between accuracy and computational costs.

5. 5.

   You have a numerical method of order 3. If the step size is reduced by half, what happens to GTE?

   Hint

   Remember the formula involving the order of the method.

6. 6.

   A simulation in engineering requires precise results. Discuss how you would choose between a second-order and a fourth-order numerical method considering GTE.

   Hint

   Think about the context of use and available resources.