17.1.1. Types of Errors

Try these first

1. 1.

   Define round-off error.

   Hint

   Think about how computers store decimal numbers.

2. 2.

   What is the local truncation error (LTE)?

   Hint

   Consider singular calculations made during solving ODEs.

3. 3.

   What causes round-off error?

   • Finite precision in arithmetic
   • Infinite precision in arithmetic
   • Human error

   Hint

   Rethink the limitations of decimal representations.

4. 4.

   True or False: The Global Truncation Error is the sum of all Local Truncation Errors at each step.

   • True
   • False

   Hint

   Consider how errors accumulate over iterations.

5. 5.

   Explain the impact of round-off error in large matrix computations and suggest a technique to minimize it.

   Hint

   Think about precision types available in programming.

6. 6.

   Given a specific example where local truncation error leads to inaccurate results, analyze the scenario.

   Hint

   Refer back to the formulas you've learned related to LTE and GTE.