Practice Convergence (18.2.3) - Stability and Convergence of Methods - Mathematics - iii (Differential Calculus) - Vol 4

Practice: Convergence

Lesson 18.2.3Stability and Convergence of Methods

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9 questions

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2 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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6 sample questions

Question 1.
What does convergence mean in numerical methods?
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Think about what happens as you take smaller and smaller steps.
Question 2.
What is the Lax Equivalence Theorem?
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Remember how consistency and stability relate to one another.
3Question 3.
What does convergence ensure in numerical methods?
- Errors grow exponentially
- Solution approaches exact solution
- Step size has no effect
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Think about the relationship between accuracy and step size.
4Question 4.
True or False: Stability is not necessary for establishing convergence.
- True
- False
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Reflect on the connection between stability and convergence.
Question 5.
Given a numerical method that failed to converge due to stability issues, identify and analyze the parameters contributing to this instability.
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Refer to the stability function of the method in question.
Question 6.
Develop a numerical method that accomplishes convergence for a given initial value problem and validate it with a specified tolerance.
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Adjust the step size dynamically to meet the tolerance level specified in the problem.

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