17.1.6. Consistency

Try these first

1. 1.

   What does consistency in numerical methods mean?

   Hint

   Consider the relationship between LTE and step size.

2. 2.

   Define local truncation error.

   Hint

   Think about how errors occur in a single approximation step.

3. 3.

   What is meant by consistency in numerical methods?

   • A) The numerical method always yields exact results.
   • B) The local truncation error approaches zero as step size approaches zero.
   • C) The error remains constant regardless of step size.

   Hint

   Think about how errors behave as calculations become finer.

4. 4.

   True or False: A consistent numerical method guarantees accurate results for all step sizes.

   • True
   • False

   Hint

   Consider if consistency alone can ensure accuracy.

5. 5.

   Suppose you have a numerical method that uses step sizes of h = 0.1 and h = 0.01. Compare the LTE at both sizes for consistency.

   Hint

   Compare the results of LTE at both h values.

6. 6.

   Discuss the implications of using a numerical method that exhibits inconsistency in a real-world application like engineering.

   Hint

   Think about what happens if calculations are inaccurate in critical structures.