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3 cards from this section. Quick, good the night before a test.
Define discretization error.
Think about the process of numerical approximation.
What is round-off error?
Consider how a calculator shows results.
What is discretization error?
Consider the main processes that lead to numerical approximations.
True or False: Round-off error can accumulate throughout numerical computations.
Think about how calculations might iterate over many steps.
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?
Consider how discretization error is impacted by both step size and numerical method stability.
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?
Identifying specific values and demonstrating the corrections is critical.
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