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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does stability in numerical methods refer to?
π‘ Hint: Think about what happens to a ship in rough waters.
Question 2
Easy
What is the significance of the Lax Equivalence Theorem?
π‘ Hint: Remember the relationship between stability and convergence.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the stability condition for a numerical method?
- |π (βπ)| β€ 1
- |π (βπ)| > 1
- |π (β)| = 1
π‘ Hint: Remember, if the stability function is greater than 1, errors will grow.
Question 2
True or False: A stable method guarantees convergence.
- True
- False
π‘ Hint: Consider the Lax Equivalence Theorem.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Derive the stability condition for a modified Euler method applied to the equation π¦' = -ππ¦, where π > 0.
π‘ Hint: Start by expressing the numerical iteration and finding the corresponding stability function.
Question 2
Apply the Backward Euler method to the equation π¦' = -2π¦ and discuss its properties, leveraging A-stability.
π‘ Hint: Evaluate the backward difference and its relation to the stability function.
Challenge and get performance evaluation