Practice Consistency, Stability, And Convergence (18.2) - Stability and Convergence of Methods

Practice: Consistency, Stability, and Convergence

Lesson 18.2Stability and Convergence of Methods

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10 questions

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3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
4 questions · about 3 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define consistency in the context of numerical methods.
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Think about how the accuracy of numerical methods improves with smaller steps.
Question 2.
What does a stable numerical method imply?
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Consider what we do with rounding errors.
3Question 3.
What is the definition of consistency in numerical methods?
- The method remains accurate regardless of step size
- The local truncation error decreases as step size decreases
- Stability is guaranteed
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Look for the relationship between step size and accuracy.
4Question 4.
Is a stable method guaranteed to converge?
- True
- False
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Recall the Lax Equivalence Theorem.
Question 5.
Consider a numerical method that has a consistent local truncation error but demonstrates growing errors due to rounding each step. Discuss the potential challenges faced in applying this method.
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Focus on the implications of error growth in larger calculations.
Question 6.
Demonstrate the implications of the Lax Equivalence Theorem in practical numerical methods by providing an example of a method that fails to converge due to lack of stability.
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Reflect on common methods in numerical algorithms and identify characteristics.

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