17.1.1.2.2. Global Truncation Error (GTE)

Try these first

1. 1.

   What does Global Truncation Error (GTE) refer to?

   Hint

   Think about what happens as we add steps in a numerical method.

2. 2.

   What is the primary formula connecting GTE and LTE?

   Hint

   Consider how we calculate total error based on single step errors!

3. 3.

   What is Global Truncation Error (GTE)?

   • Error in a single step
   • Cumulative error over multiple steps
   • Error from round-off

   Hint

   Consider what happens when you keep approximating.

4. 4.

   True or False: GTE is independent of the step size used in the numerical method.

   • True
   • False

   Hint

   Reflect on the relationship between step size and error.

5. 5.

   Consider a numerical method with a high order, how would you adjust your approach to maintain low GTE while solving complex ODEs?

   Hint

   Evaluate the function’s responsiveness and detail when changing steps.

6. 6.

   Given an ODE solved using Euler's method yielding GTE as O(h), derive the implications on choosing h for an error threshold of 0.01.

   Hint

   How does the total error influence your step sizes?