Practice Types of Stability - 18.3 | 18. Stability and Convergence of Methods | Mathematics - iii (Differential Calculus) - Vol 4
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is zero-stability?

💡 Hint: Think about the effect of small rounding errors.

Question 2

Easy

Name a method that is A-stable.

💡 Hint: Consider implicit methods.

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 defines zero-stability in a numerical method?

  • Solutions grow uncontrollably
  • No growth due to small errors
  • Only valid for linear equations

💡 Hint: Focus on the consequences of small errors.

Question 2

True or False: A-stability means a method is stable for all Re(λ) < 0.

  • True
  • False

💡 Hint: Review what A-stability is focused on.

Solve 2 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Consider the difference between a zero-stable method and an A-stable method. Provide a scenario illustrating when you would choose each type.

💡 Hint: Reflect on the properties of the equations you typically encounter.

Question 2

Why might an L-stable method provide a significant advantage when solving a stiff differential equation? Provide an example of such an equation.

💡 Hint: Consider situations where stiffness arises in real-world problems.

Challenge and get performance evaluation