Practice Stability of Common Methods - 18.4 | 18. Stability and Convergence of Methods | Mathematics - iii (Differential Calculus) - Vol 4
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Stability of Common Methods

18.4 - Stability of Common Methods

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Practice Questions

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Question 1 Easy

What is the stability function for Euler's Method?

💡 Hint: Think about the general form of stability functions.

Question 2 Easy

Define A-stability.

💡 Hint: What does it mean for a method to handle certain values of λ?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What defines the condition of a method being A-stable?

It is stable for Re(λ) < 0
It requires large step sizes
It is stable for Re(λ) > 0

💡 Hint: Think about the real part of λ and its relation to A-stability.

Question 2

True or False: All numerical methods are conditionally stable.

True
False

💡 Hint: Consider what makes a numerical method reliable.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Assess the stability of the Midpoint method if h = 1 and λ = -3. Show your calculations clearly.

💡 Hint: Recall how to derive R(z) for the midpoint method.

Challenge 2 Hard

Discuss the impact of the Lax Equivalence Theorem on the design of numerical methods.

💡 Hint: What does this mean for method selection when solving ODEs?

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