17.1.1.3. Discretization Error

Try these first

1. 1.

   Define discretization error.

   Hint

   Think about the process of numerical approximation.

2. 2.

   What is round-off error?

   Hint

   Consider how a calculator shows results.

3. 3.

   What is discretization error?

   Hint

   Consider the main processes that lead to numerical approximations.

4. 4.

   True or False: Round-off error can accumulate throughout numerical computations.

   • True
   • False

   Hint

   Think about how calculations might iterate over many steps.

5. 5.

   Given a differential equation solved numerically using explicit methods, describe the discrepancies arising from discretization error when changing the step size from h to h/2. What implications does this have for solution accuracy?

   Hint

   Consider how discretization error is impacted by both step size and numerical method stability.

6. 6.

   Analyze a case where a numerical solution diverges significantly from an analytical solution. What role does discretization error play in this divergence, and how could you approach correcting it?

   Hint

   Identifying specific values and demonstrating the corrections is critical.